Jack,
I've not heard of that issue before. The SCLogin module calls some code out of JFBConnect for performing the login. The whole login process is initiated through Javascript and the last step is to redirect the user to:
index.php?option=com_jfbconnect&task=loginFacebookUser
That step is required and it should cause the page to refresh. Server side caching shouldn't prevent that at all and neither should browser caching.
In short, I'm not sure why the page wouldn't refresh. Can you help answer a few questions so I can narrow things down further:
* If you disable caching on your server, does the issue go away?
* When you refresh, are you logged in already *or* does the page reload itself again? If you have the "Show 'Logging in' Popup" setting enabled, when does that popup appear (when you click the Login with Facebook button or when you refresh)?
With the answers above, we should be able to help you get to the bottom of things.
Thanks,
Alex