Except the way the Persona protocol is designed means that Mozilla doesn't know either.

As someone else pointed out, Mozilla won't have to know once the protocol is more supported. Currently they're acting as a transitionary bridge, not a required element.

Also, iirc, Google doesn't have to know where you're signing in either. I'll have to double check that part.

The identity provider/bridge doesn't know either. They sign an assertion, so they know that you want to log in somewhere once, but not where or when.