Rich,
Not sure about the Autotune issue. It doesn't sound critical though, so we can come back to that if there's some setting you need to update through Autotune.
For auto-login, it likely is working. There are some safeguards in JFBConnect to prevent users from being automatically logged back in if they intentionally logged out. Please try logging into Facebook.com in another browser and then visiting your site. It will likely work. Alternatively, you can clear the cache in your browser, do a full exit (to clear all cookies) and then restart and try again. My guess is that will work as well.
Let me know if that helps,
Alex