After debugging I was able to notice that the actions for the $form[submit] element differ from the $form[overview] (which is the form element for the "Save and go to list" button.
A "dirty" change and quick patch to include the "permissions_by_term_submit" action onto the list for the "Overview" element.
If the change proposed could be improved, please don't hesitate and ping me, I'll be glad to learn.