wpse-273548-controls.js

var wpse273548controls = (function ( api ) {
	'use strict';

	var component = {};

	/**
	 * Init.
	 *
	 * @returns {void}
	 */
	component.init = function() {
		api.bind( 'ready', component.ready );
	};

	/**
	 * Ready.
	 *
	 * @returns {void}
	 */
	component.ready = function() {
		api.previewedDevice.bind( component.sendPreviewedDevice );
		api.previewer.bind( 'ready', component.sendPreviewedDevice );
	};

	/**
	 * Handle change of previewed device.
	 * @returns {void}
	 */
	component.sendPreviewedDevice = function() {
		api.previewer.send( 'previewed-device', api.previewedDevice.get() );
	};

	return component;

}) ( wp.customize );

wpse-273548-preview.js

var wpse273548preview = (function ( api , $) {
	'use strict';

	var component = {
		previousPreviewedDevice: null
	};

	/**
	 * Init.
	 *
	 * @returns {void}
	 */
	component.init = function() {
		api.bind( 'preview-ready', function() {
			api.preview.bind( 'previewed-device', component.handlePreviewedDeviceChange );
		} );
	};

	/**
	 * Handle previewed device change.
	 *
	 * @param {string} previewedDevice Previewed device.
	 * @returns {void}
	 */
	component.handlePreviewedDeviceChange = function( previewedDevice ) {
		var body = $( document.body );
		if ( component.previousPreviewedDevice ) {
			body.removeClass( component.previousPreviewedDevice );
		}
		body.addClass( previewedDevice );
		component.previousPreviewedDevice = previewedDevice;
	};

	return component;
}) ( wp.customize, jQuery );

wpse-273548.php

<?php
/**
 * Plugin Name: Toggle class name on body based on previewed device in Customizer
 * Plugin URI: https://wordpress.stackexchange.com/questions/273548/detect-device-change-desktop-tablet-or-mobile-in-customizer
 * Author: Weston Ruter, XWP
 * Author URI: https://make.xwp.co/
 * License: GPLv2+
 */

/*
 * Copyright (c) 2017 XWP (https://make.xwp.co/)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License, version 2 or, at
 * your discretion, any later version, as published by the Free
 * Software Foundation.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 */

// Add controls script.
add_action( 'customize_controls_enqueue_scripts', function() {
	$handle = 'wpse-273548-controls';
	$src = plugin_dir_url( __FILE__ ) . '/wpse-273548-controls.js';
	$deps = array( 'underscore', 'customize-controls' );
	wp_enqueue_script( $handle, $src, $deps );
	wp_add_inline_script( $handle, 'wpse273548controls.init();' );
} );

// Add preview script.
add_action( 'wp_enqueue_scripts', function() {
	global $wp_customize;
	if ( ! is_customize_preview() ) {
		return;
	}
	$handle = 'wpse-273548-preview';
	$src = plugin_dir_url( __FILE__ ) . '/wpse-273548-preview.js';
	$deps = array( 'underscore', 'customize-preview' );
	wp_enqueue_script( $handle, $src, $deps );
	wp_add_inline_script( $handle, 'wpse273548preview.init();' );
} );