Autologin should work like you describe to automatically login a user that has already registered with Facebook on your site.
However, please note that when you Log out of your site, JFBConnect will not automatically log you back in. There is a time out to prevent that, otherwise a user wouldn't be able to logout. They'd click logout and JFBConnect would automatically log them back in which would be quite frustrating.
The best way to test the automatic login feature is to:
* Clear your browser history (or test in a different browser)
* Login to Facebook.com
* Visit your website. JFBConnect should automatically log you in
I hope that helps explain, but if you test and are still having issues, please let us know.
Thanks,
Alex