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

How to use custom PHP code?
PHP code can be added to your (child) theme's functions.php file. Alternatively, you can use the Custom Hooks add-on, or a code snippets plugin. More info
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