Depends on https://github.com/xwp/wp-customize-partial-refresh/pull/17 • Demo video: https://www.youtube.com/watch?v=hb3uezGTzFc

class-wp-customize-rich-text-control.php

<?php
/**
 * WP_Customize_Rich_Text_Control class
 *
 * @package WelcomeMessage
 */

namespace WelcomeMessage;

/**
 * Customize Rich Text Control class.
 *
 * @see \WP_Customize_Control
 */
class WP_Customize_Rich_Text_Control extends \WP_Customize_Control {

	/**
	 * Control type.
	 *
	 * @since 4.2.0
	 * @access public
	 * @var string
	 */
	public $type = 'rich_text';

	/**
	 * Editor arguments.
	 *
	 * @see \_WP_Editors::parse_settings()
	 * @var array
	 */
	public $editor_arguments = array();

	/**
	 * Constructor.
	 *
	 * @since 4.1.0
	 * @since 4.2.0 Moved from WP_Customize_Upload_Control.
	 *
	 * @param \WP_Customize_Manager $manager Customizer bootstrap instance.
	 * @param string                $id      Control ID.
	 * @param array                 $args    Optional. Arguments to override class property defaults.
	 */
	public function __construct( $manager, $id, $args = array() ) {

		if ( ! isset( $args['editor_arguments'] ) ) {
			$args['editor_arguments'] = array();
		}

		$args['editor_arguments'] = wp_parse_args( $args['editor_arguments'], array(
			'teeny' => true,
		) );

		parent::__construct( $manager, $id, $args );
	}

	/**
	 * Enqueue control related scripts/styles.
	 */
	public function enqueue() {

		$handle = 'customize-rich-text-control';
		$src = plugin_dir_url( __FILE__ ) . '/customize-rich-text-control.js';
		$deps = array( 'customize-controls', 'editor' );
		$ver = false;
		$in_footer = true;
		wp_enqueue_script( $handle, $src, $deps, $ver, $in_footer );

		add_action( 'customize_controls_print_footer_scripts', array( $this, 'render_editor' ), 0 );

		// @todo These should be included in \_WP_Editors::editor_settings()
		if ( false === has_action( 'customize_controls_print_footer_scripts', array( '_WP_Editors', 'enqueue_scripts' ) ) ) {
			add_action( 'customize_controls_print_footer_scripts', array( '_WP_Editors', 'enqueue_scripts' ) );
		}
	}

	/**
	 * Render rich text editor.
	 */
	public function render_editor() {
		echo '<div hidden>';
		wp_editor( '', "$this->id-customize-rich-text-control", $this->editor_arguments );
		echo '</div>';
	}

	/**
	 * Refresh the parameters passed to the JavaScript via JSON.
	 *
	 * @since 3.4.0
	 * @since 4.2.0 Moved from WP_Customize_Upload_Control.
	 *
	 * @see WP_Customize_Control::to_json()
	 * @return array Exported data.
	 */
	public function json() {
		$exported = parent::json();
		$exported['editor_arguments'] = $this->editor_arguments;
		return $exported;
	}

	/**
	 * Override render_content to be no-op since content is exported via to_json for deferred embedding.
	 */
	public function render_content() {}

	/**
	 * An Underscore (JS) template for this control's content (but not its container).
	 *
	 * Class variables for this control class are available in the `data` JS object;
	 * export custom variables by overriding {@see WP_Customize_Control::to_json()}.
	 *
	 * @see WP_Customize_Control::print_template()
	 */
	protected function content_template() {
		?>
		<label for="{{ data.settings['default'] }}-button">
			<# if ( data.label ) { #>
				<span class="customize-control-title">{{ data.label }}</span>
			<# } #>
			<# if ( data.description ) { #>
				<span class="description customize-control-description">{{{ data.description }}}</span>
			<# } #>
		</label>

		<div class="wp-editor-placeholder"></div>
		<?php
	}
}

customize-rich-text-control.js

/* global wp, jQuery, tinyMCE */
(function( api, $ ) {

	// @todo Is there a better way to listen for when TinyMCE has finished initializing the editors?
	var windowLoaded = $.Deferred();
	$( window ).on( 'load', function() {
		tinyMCE.on( '' );
		windowLoaded.resolve();
	} );

	/**
	 * @class
	 *
	 * @todo Populate with initial content
	 * @todo Update setting when rich text editor changes.
	 */
	api.controlConstructor.rich_text = api.Control.extend({

		/**
		 * Render the content and inject the TinyMCE editor into the control.
		 */
		renderContent: function() {
			var control = this;
			api.Control.prototype.renderContent.call( control );
			control.container.find( '.wp-editor-placeholder' ).replaceWith( $( '#wp-' + control.id + '-customize-rich-text-control-wrap' ) );
		},

		/**
		 * Embed the control into the page.
		 */
		embed: function() {
			var control = this,
				inject;

			// Watch for changes to the section state
			inject = function( sectionId ) {
				var parentContainer;
				if ( ! sectionId ) { // @todo allow a control to be embedded without a section, for instance a control embedded in the frontend
					return;
				}

				// Wait for the section to be registered
				api.section( sectionId, function( section ) {
					var deferredDependencies = [ windowLoaded, section.deferred.embedded ];

					// Wait for the window to load (and thus the Tiny MCE editor) and the section to be ready/initialized
					$.when( deferredDependencies ).then( function() {

						parentContainer = section.container.find( 'ul:first' );
						if ( ! control.container.parent().is( parentContainer ) ) {
							parentContainer.append( control.container );
							control.renderContent();
						}

						// @todo tinyMCE.onAddEditor?
						setTimeout( function() {
							control.deferred.embedded.resolve();
						}, 1000 );
					});
				});
			};

			control.section.bind( inject );
			inject( control.section.get() );
		},

		/**
		 * Ready.
		 */
		ready: function() {
			var control = this, editor = control.getEditor(), element, suspendRecursion;

			element = new api.Element( $( '#' + control.id + '-customize-rich-text-control' ) );
			control.elements.push( element );
			element.set( control.setting() );
			element.sync( control.setting );

			control.setting.bind( function( value ) {
				if ( ! suspendRecursion ) {
					editor.setContent( value );
				}
			} );

			if ( editor ) {
				editor.setContent( control.setting() );
				editor.on( 'input change keyup', function() {
					var value = wp.editor.removep( editor.getContent() );
					suspendRecursion = true;
					control.setting.set( value );
					suspendRecursion = false;
				} );
			} else {
				// @todo Initialize when the editor gets added.
			}
		},

		/**
		 * Get the tinyMCE editor for this control.
		 *
		 * @returns {tinyMCE.Editor|null}
		 */
		getEditor: function() {
			var control = this;
			return tinyMCE.get( control.id + '-customize-rich-text-control' );
		},

		/**
		 * Focus on editor content.
		 *
		 * @param {Object}   [params]
		 * @param {Function} [params.completeCallback]
		 */
		focus: function( params ) {
			var control, completeCallback, focus;
			control = this;
			params = params || {};
			focus = function() {
				var editor = control.getEditor();
				if ( editor ) {
					control.container[0].scrollIntoView();
					editor.focus();
				} else {

					// Fallback in case the editor hasn't been initialized yet.
					control.container.find( 'input, select, textarea, button, object, a[href], [tabindex]' ).filter( ':visible' ).first().focus();
				}
			};
			if ( params.completeCallback ) {
				completeCallback = params.completeCallback;
				params.completeCallback = function() {
					focus();
					completeCallback();
				};
			} else {
				params.completeCallback = focus;
			}
			if ( control.expand ) {
				control.expand( params );
			} else {
				params.completeCallback();
			}
		}
	});

}( wp.customize, jQuery ) );

welcome-message-preview.js

/* global wp */
(function( api ) {

	api.bind( 'preview-ready', function() {
		// @todo We can initialize a TinyMCE editor in the preview.
	} );

}( wp.customize ) );

welcome-message.php

<?php
/**
 * Plugin name: Welcome Message
 * Description: Demonstration of selective refresh in the Customizer.
 * Author: Weston Ruter, XWP
 * Plugin URL:
 *
 * @todo Let this be FooterText instead
 *
 * @package WelcomeMessage
 */

namespace WelcomeMessage;

/**
 * Render the welcome message.
 *
 * This function can be used in the template directly.
 * This function is called after the associated Customizer setting has already
 * been previewed, so we can call it just as if we were in the template normally.
 *
 * @see \get_template_part()
 */
function the_welcome_message() {
	// @todo What about the before/after container?
	echo apply_filters( 'the_content', get_option( 'welcome_message' ) );
}

/**
 * Add welcome message container to document before sidebar.
 */
function add_welcome_message_container() {
	echo '<div class="welcome-message">';
	the_welcome_message();
	echo '</div>';
}
add_action( 'get_sidebar', __NAMESPACE__ . '\add_welcome_message_container' );

/**
 * Enqueue preview scripts.
 */
function enqueue_preview_scripts() {
	$handle = 'welcome-message-preview';
	$src = plugin_dir_url( __FILE__ ) . '/welcome-message-preview.js';
	$deps = array( 'customize-preview' );
	$ver = false;
	$in_footer = true;
	wp_enqueue_script( $handle, $src, $deps, $ver, $in_footer );
}
add_action( 'customize_preview_init', function() {
	add_action( 'wp_enqueue_scripts', __NAMESPACE__ . '\enqueue_preview_scripts' );
} );

/**
 * Register selective refresh partial.
 *
 * @param \WP_Customize_Manager $wp_customize Manager.
 */
function register_selective_refresh_partial( \WP_Customize_Manager $wp_customize ) {

	require_once __DIR__ . '/class-wp-customize-rich-text-control.php';
	$wp_customize->register_control_type( __NAMESPACE__ . '\WP_Customize_Rich_Text_Control' );

	$customize_id = 'welcome_message';

	$wp_customize->add_setting( $customize_id, array(
		'type' => 'option',
		'transport' => 'postMessage',
	) );

	$wp_customize->add_control( new WP_Customize_Rich_Text_Control( $wp_customize, $customize_id, array(
		'label' => __( 'Welcome Message' ),
		'settings' => $customize_id,
		'section' => 'title_tagline',
	) ) );

	if ( isset( $wp_customize->selective_refresh ) ) {
		$wp_customize->selective_refresh->add_partial( 'welcome_message', array(
			'selector' => '.welcome-message',
			'settings' => array( $customize_id ),
			'render_callback' => __NAMESPACE__ . '\the_welcome_message',
		) );
	}
}
add_action( 'customize_register', __NAMESPACE__ . '\register_selective_refresh_partial', 100 );