Thanks for the video, it helps understand how you're testing a bit. The browser area was a little cutoff, so I didn't get to see everything though, but I think I see some issues.
First, we've been trying to recreate this and have been unable to under various situations. We are testing on a site with CB with field mappings and such and tried to match up as much as we could.
The one thing from your video that stands out is that, when you click the logout button, there was an error page. I'm assuming from there you're clicking the "Back" button. In that case, since there was an error, the full logout process may not have been completed by Joomla. This could easily be leaving a session open inside Joomla. When you next login via Twitter, the session data from the previous user may be fetched from Joomla and used by JFBConnect. In that case, JFBConnect would simply think the 'old' user is still logged in and trying to add his Twitter account to his existing Joomla account.
That would explain why the fields are imported and why the connection between the accounts is being made.
When the logout process occurs normally, all session data for a user should be destroyed. That's taken care of by Joomla. That way, on the next page load, JFBConnect would think there is a completely new visitor to the site.. there's be no state variables associated with the previous user. Running into an error on logout (possibly not clearing the session) and then hitting the back button (possibly sending the 'old' user's session cookie) is the only thing I can see from your video that would explain the issue.
In that case, I'd have to stress to you to fix the error. Then, even the back button shouldn't cause problems. I'd still test without hitting the back button at first though.
The other thing I dont really understand why Google button still appears after I logging in using Twitter. Why is the Google login button still there?
JFBConnect lets logged in users associate their current account to other social networks that they haven't already connected to. This lets them login with that social network later.
If you don't want that feature, disable the "Show Connect Account Button(s)" setting in the SCLogin -> Logout parameters area.
I hope that helps explain, but let me know if you still run into issues.. or let me know a lot more about what the logout error in your video is.
Thanks,
Alex