Add the following code to your (child) theme’s functions.php to fade (in / out) the template content during refresh:

add_action( 'wp_head', function() {
?>
    <script>
      (function($) {
        $(document).on('facetwp-refresh', function() {
          $('.facetwp-template').animate({ opacity: 0 }, 1000);
        });
        $(document).on('facetwp-loaded', function() {
          $('.facetwp-template').animate({ opacity: 1 }, 1000);
        });
      })(jQuery);
    </script>
<?php
}, 100 );

See also