Hmmmmmmmmm. Not a good way for me to start a response, but that's how I'm going for it
You shouldn't see the "Connect this account with Facebook" link if you logged in with Facebook. That's actually a little worrysome. Can you verify that the account your logging in with (via JFBConnect/Facebook) is actually logged in correctly by going to your user details page at:
index.php?option=com_user&view=user&layout=form
You should see your expected Joomla username (either what you chose at registration or fb_12345, depending on your JFBConnect User Creation configuration) and, likely, your Facebook email address. If you're not seeing that, let me know. It's possible the user mapping between your Joomla User account and your Facebook account is not occurring properly within JFBConnect. It's not normal, but if it's happening, we want to fix it.
As for an explanation and some more information... that message should only appear if you log in as a Joomla user and that Joomla User has no mapping to a Facebook account on your site (through JFBConnect). When you are a Joomla user with no Facebook account mapped, we present the link to allow that user to 'connect' the 2 accounts, and then later, when they return, they can log in either through Joomla or Facebook.
I'm pretty sure, though I'd have to verify, that if you've ever logged in through Facebook and associated it with a Joomla user (or did a fresh registration with that Facebook account) that you shouldn't see the "reconnect" link.
Most importantly, and to answer one of your questions, in the JFCLogin module, there is an option to "Allow reconnections". Disabling it should get rid of that link. However, please test, because the description you give above may be problematic, but it's late, and I may be reading it incorrectly.
Hope this lengthy answer helps!