Alter the date presented within month view tooltips for multiday events.

modifiy-multiday-event-tooltips.php

<?php
/**
 * Modifies the month view tooltip for multiday events.
 *
 * Instead of seeing "5 - 15 August", the tooltip for multiday event will show
 * the date of the cell which contains it.
 *
 * For example, if a visitor hovers over the multiday event name within the cell
 * for 11 August, the tooltip will now display "11 August" etc.
 */
class Month_View_Multiday_Event_Tooltip_Modifier {
	private $current_day;

	public function __construct() {
		add_filter( 'tribe_events_get_current_month_day', [ $this, 'capture_day' ] );
		add_filter( 'tribe_events_template_data_array', [ $this, 'replace_date' ], 10, 2 );
	}

	public function capture_day( $day ) {
		$this->save_formatted_day( $day );
		return $day;
	}

	private function save_formatted_day( $day ) {
		if ( ! is_array( $day ) || empty( $day['date'] ) ) {
			$this->current_day = '';
			return;
		}

		$this->current_day = tribe_format_date( $day['date'] );
	}

	public function replace_date( $tooltip_data, $event = false ) {
		if ( ! $event ) {
			return $tooltip_data;
		}

		if ( tribe_event_is_multiday( $event->ID ) && ! empty( $this->current_day ) ) {
			$tooltip_data['dateDisplay'] = $this->current_day;
		}

		return $tooltip_data;
	}
}

new Month_View_Multiday_Event_Tooltip_Modifier;