In the Configuration area of JFBConnect, in the Login/Logout tab, simply change "Auto Login Facebook Users" to No.
The problem of not being able to logout happens if you're using a Logout button that's not from JFBConnect. Our logout button calls a little extra Javascript to log the user out of Facebook, which prevents them from automatically being logged back in (since they'd remain logged into Facebook). If you can't use our logout button, then yes, you should disable that option.
Hope that helps,
Alex