I'm not sure what you mean by it's bigger than Facebook. Twitter, LinkedIn and most other social networks allow importing the user's email address. If automatic registration is enabled, then they will bypass the login or register page.
Some networks, like Instagram, don't allow the email to be imported though. You can make a code adjustment to force an Itemid onto that URL. That Itemid could be for any menu item you have and then you could assign modules to that menu item just for JFBConnect. To do so, edit the /components/com_jfbconnect/controllers/login.php file. Around line 123 you'll see:
$app->redirect(JRoute::_('index.php?option=com_jfbconnect&view=loginregister&provider=' . strtolower($provider->name) . '&return=' . base64_encode($return), false));
Update that with the right Itemid, like:
$app->redirect(JRoute::_('index.php?option=com_jfbconnect&view=loginregister&Itemid=XXX&provider=' . strtolower($provider->name) . '&return=' . base64_encode($return), false));
I hope that helps,
Alex