Facebook removed the ability fetch a user's cover photo a few years back. However, they recently re-introduced a way to fetch it again. We haven't tested the new way yet, but it's on our to-do list to implement.
As it stands now, JFBConnect should only be fetching a cover photo from Twitter. The avatar for the user can come from multiple social networks, depending on how they register or login.
For updating the avatar, it should be updated if you have the "Always import profile" setting enabled. When enabled, all fields currently configured and avatar should be updated on new logins. If disabled, their profile will only be fetched when they first register.
I hope that helps,
Alex