This will work with any of the Popup Maker newsletter integration extensions. This will close the popup when the form is submitted successfully.

functions.php

<?php
add_action( 'wp_footer', 'my_custom_popup_scripts', 500 );
function my_custom_popup_scripts() { ?>
	<script type="text/javascript">
		(function ($) {

			$('.pum_sub_form').on('pumNewsletterSuccess pumNewsletterErrorAlreadySubscribed', function () {
				$(this).parents('.popmake').popmake('close');
			});


		}(jQuery))
	</script><?php
}