If you have it set to Full Joomla User, the user clicks the button and goes to the Login/Register page but doesn't do anything there (clicks a difrerent link, closes browser, etc), there will be no trace of that user in your Joomla site. No user, no mapping (nothing to map too).
The only thing that's happened is that the user has approved your application, so if they click the blue button again, they'll skip that step. However, when they click it again, they'd then be redirected to the Login/Register page to try again.
Hope that explains it, and good luck,
Alex
Redirect for new FB users to registration page
