The Events Calendar List View Multi Day Events Show Today as the Start Date

list-view-start-tribe.php

<?php
/*
Plugin Name: A Snippet for List View Multi Day Events Start Time - The Events Calendar
Plugin URI: http://theeventscalendar.com
Description: This plugin changes the List View Start Times for Multiple Day Events.
Author: brianjessee
Version: 1.0
Author URI: http://theeventscalendar.com
*/
/**
 * Example if an Event runs from May 1st to June 31st when visiting the list view on June 10th
 * it looks like the first event is in May, but it is currently June. This snippet changes it
 * so it displays JUne 10th as the start date in the list view.
 */
 
if ( ! function_exists( 'tribe_get_start_date' ) ) {
	/**
	 * Start Date
	 *
	 * Returns the event start date and time
	 *
	 * @category Events
	 *
	 * @param int    $event        (optional)
	 * @param bool   $display_time If true shows date and time, if false only shows date
	 * @param string $date_format  Allows date and time formating using standard php syntax (http://php.net/manual/en/function.date.php)
	 * @param string $timezone     Timezone in which to present the date/time (or default behaviour if not set)
	 *
	 * @return string|null Date
	 */
	function tribe_get_start_date( $event = null, $display_time = true, $date_format = '', $timezone = null ) {
		if ( is_null( $event ) ) {
			global $post;
			$event = $post;
		}

		if ( is_numeric( $event ) ) {
			$event = get_post( $event );
		}

		if ( ! is_object( $event ) ) {
			return '';
		}

		if ( Tribe__Date_Utils::is_all_day( get_post_meta( $event->ID, '_EventAllDay', true ) ) ) {
			$display_time = false;
		}

		// @todo move timezones to Common
		if ( class_exists( 'Tribe__Events__Timezones' ) ) {
			$start_date = Tribe__Events__Timezones::event_start_timestamp( $event->ID, $timezone );
		} else {
			return null;
		}

		if ( tribe_is_list_view() && ! tribe_is_past() ) {
			//echo $start_date . ' start <br>';
			$blogtime = current_time( 'mysql' );
			//echo strtotime( $cc_blogtime ) . ' mysql <br>';
			if ( $start_date > $blogtime ) {
				//echo $start_date . 'less <br>';
				$start_date = $blogtime;
				//echo $start_date . 'new <br>';
			}
		}
		return tribe_format_date( $start_date, $display_time, $date_format );
	}
}

This tweaked version might be helpful as well:
https://gist.github.com/andrasguseo/d252c9e0c85c96e5a2bcfe36b0d09031