Yes, the video is showing strange behavior. When an existing user is mapped to a social network, they should not be redirected back to that login/register view, even if Same Page is selected. I checked the behavior on my test site and was redirected back to the homepage, not the loginregister view.
1. For sanity, could you verify what the "New User Redirection" setting is set to?
2. Looking at the code for this mapping, if there's a failure in the login, it's redirected to that login/register view instead of the redirection setting. From your behavior, it seems like a possibility is that the user might not have been logged in properly, even though the avatar and name show up. Could you look to see if there are any other system plugins that may redirect on login, such as JomSocial Redirect system plugin?
-Melissa