Ivan,
I'm not sure. There really shouldn't be anything within JFBConnect that's trying to communicate about the user in the admin area. We don't allow logins to the admin area and I can't think of any reason that a query on the user's behalf would be made.
Can you try to put some debugging into the /components/com_jfbconnect/libraries/facebook.php file's api function to see if you can get more information about what query to Facebook is being made? Without that, I'm just not sure what's going on.
Thanks,
Alex