We've had the auto-login timeout feature for at least 6 months (since v5.0.0) and I think even longer. You shouldn't have been automatically logged in before right after logging out. If you were, *that* was a bug. The behavior you describe now sounds correct.
I hope that helps, and glad things are working how you only dreamed they would

As always though, should you need anything else, just let us know.
Finally, if you haven't already, please consider leaving a rating and review for JFBConnect, or our support, on the Joomla Extension Directory. It certainly isn't required, but is very appreciated:
extensions.joomla.org/extensions/social-...ook-integration/7215
Thanks,
Alex