Is there an Authcache load event for fragments?
If you register your JavaScript as a behavior, then it is executed whenever the DOM changes, also when a fragment was loaded by authcache (see Managing JavaScript in Drupal 7). For example, the proper way to process any view - regardless of whether it is loaded via Authcache or not works something like this:

(function ($, Drupal) {
  "use strict";
  Drupal.behaviors.exampleModule = {
    attach: function (context, settings) {
      $('.view', context).once(function () {
        var view = $(this);
        // do something with view.
      });
    }
  };
}(jQuery, Drupal));