When you enable the Automatic registration feature, that should automatically create a new Joomla account for the user if they don't already have one. The only exception to this is Twitter, since it doesn't provide an email address. In that case, the user must go through a form-based registration to at least provide their email address.
I just tried to register and was brought to the standard Joomla registration page. That shouldn't normally happen with JFBConnect as it shouldn't ever redirect to that page. We have our own registration page that we use for registration, when required.
Can you tell me:
* Do you have any profile management extensions on your site (Community Builder, JomSocial, etc)?
* Do you have any System or User plugins that alter the registration process or are meant to redirect the user when they are logging in? If so, try to disable them.
If none of those help narrow things down, we'll have to ask for admin credentials to your site to investigate further.
Thanks,
Alex