That's the correct behavior. When you log out of your site, you are still logged into Facebook. Therefore, when you click the Facebook login button again, Facebook already knows that you are logged in and simply passes your information back to our site. If you go to Facebook.com, you'll see you're logged in.
To do what you're looking for, either:
* Disable the "Logout of Joomla Only" setting in the Configuration -> Facebook area of JFBConnect. When disabled, the user will be logged out of your site *and* Facebook when they logout on one of your pages.
* After you logout on your site, navigate to Facebook.com and logout there. Then, when you login to your site again with Facebook, a popup will appear asking for the user's Facebook credentials
I hope that helps explain,
Alex