Disable cache for one JS file / library
I can not believe that you will have one different JS for every group. So caching is cool, and I assume your problem is the triggering of a function in the JS. 

You can use the Drupal.behaviors to call a function in your JS everytime a page is loaded, i.e.

(function ($, Drupal) {

  Drupal.behaviors.anyInit = {
      attach: function () {
        myInitFunction();
      }
  }
})(jQuery, Drupal);

function myInitFunction() { do something }


And you can pass variables to the JS (like your group name), by attaching them to your rendering array, like so:

$build['#attached']['library'][] = 'bootasde/asdejs';
$build['#attached']['drupalSettings']['bootasde']['proreos_server'] = SystemTools::getProreosServer();
$build['#attached']['drupalSettings']['bootasde']['checktyp'] = 'a';
$build['#attached']['drupalSettings']['bootasde']['id'] = $id;


Then you access that variables in your JS like:

  var server = drupalSettings.bootasde.proreos_server;
  var id = drupalSettings.bootasde.id;
  var tp = drupalSettings.bootasde.checktyp;


Hope that helps.

Another way could be to add the group names to the CSS classes in your twig template and have some special selectors for each groupname.