So to rehash, when you log in, on Facebook you're one user, but on the site you're a different user than you'd expect.
This could definitely be caused by allow reconnections being enabled. If you're only importing the profile on registration, it would not update the 'wrong' Joomla user's profile with the avatar from Facebook, and instead leave it at the original user's picture.
However, it seems like we might be missing something else here. How are you logging in both times, with Facebook, or are you trying to log in with Joomla as well? Do you have JFBConnect set to log the user out of Facebook and Joomla, or just Joomla? It's possible a combination of these settings are working against each other to remap accounts at unexpected times. However, if you are logging out and back in, it shouldn't be a re-connection at that point.. simply a login.
If it is some sort of conflict, we can check for that configuration and throw a warning to the admin that invalid options are set. We like all 3 (enable reconnects, logout of only Joomla, and automatic login via Facebook), but I can walk through in my head how all 3 could end up with a problem:
1) Login to site with Facebook - Joomla User associated with correct FB User
2) Logout of Facebook on Facebook's site (remaining logged into Joomla)
3) Login to Facebook with different account and revisit page
At this point, if automatic login is enabled AND reconnections are allowed, it may remap the user. We'd have to check.
Let us know if this seems similar, or something else might be going on.
Thanks for the feedback!