Jeroen,
Not sure what version of JFBConnect you're using, but the auto-login redirect problem was fixed a few versions ago. It only affected a few sites, because the redirection to the index.php only happened under certain configuration circumstances, if I recall. Either way, it isn't a problem anymore.
Additionally, that whole redirection logic has been moved into the /controllers/loginregister.php file into a common function that all login routes take (auto, full joomla user, facebook only), which makes the logic a lot simpler than we were doing before.
Thanks for your code change though, and hopefully it will help others if they're using an older version.