This is the code you can use to display the proper error messages for Modern Tribe's The Events Calendar add-ons. Instructions included in the comments below.

gistfile1.php

<?php
/**
 * In the root plugin file, where you initialize your class on 'plugins_loaded', run a check 
 * to see if class TribeEvents exists, if it doesn't, show the error message. This takes 
 * care of if TEC is not installed. The below code is an example from 
 * The Events Calendar: Community Events.
 */
///////////////////
// File: the-events-calendar-community-events/tribe-community-events.php
///////////////////

// ...
 
 /**
 * Instantiate class and set up WordPress actions.
 */
function Tribe_CE_Load() {
  if ( class_exists( 'TribeEvents' ) && defined( 'TribeEvents::VERSION' ) ) {
		TribeCommunityEvents::instance();
	} else {
		add_action( 'admin_notices', 'tribe_ce_show_fail_message' );
	}
}

/**
 * Shows message if the plugin can't load due to TEC not being installed.
 */
function tribe_ce_show_fail_message() {
	if ( current_user_can( 'activate_plugins' ) ) {
		$url = 'plugin-install.php?tab=plugin-information&plugin=the-events-calendar&TB_iframe=true';
		$title = __( 'The Events Calendar', 'tribe-events-community' );
		echo '<div class="error"><p>'.sprintf( __( 'To begin using The Events Calendar: Community Events, please install the latest version of <a href="%s" class="thickbox" title="%s">The Events Calendar</a>.', 'tribe-events-community' ), $url, $title ) . '</p></div>';
	}
}

add_action( 'plugins_loaded', 'Tribe_CE_Load', 1 ); // high priority so that it's not too late for tribe_register-helpers class

//...

///////////////////



/**
 * To the main class of the add-on, hook in an init_addon() method to the hook 'tribe_tec_addons'.
 * This takes care of making sure the versions line up.
 * This is the excerpt from the Community Events main class file. 
 */
///////////////////
// File: the-events-calendar-community-events/tribe-community-events.class.php
///////////////////

// ...

/**
 * The current version of Community Events
 */
const VERSION = '1.0.6';
		
/**
 * required The Events Calendar Version
 */
const REQUIRED_TEC_VERSION = '3.0';

// ...

add_filter( 'tribe_tec_addons', array( $this, 'init_addon' ) );

// ...

public function init_addon( $plugins ) {
  $plugins['TribeCE'] = array( 
    'plugin_name' => 'The Events Calendar: Community Events', 
    'required_version' => TribeCommunityEvents::REQUIRED_TEC_VERSION, 
    'current_version' => TribeCommunityEvents::VERSION, 
    'plugin_dir_file' => basename( dirname( dirname( __FILE__ ) ) ) . '/tribe-community-events.php' 
  );
  return $plugins;
}

// ...

///////////////////