I think you might be confused with how Persona works, it's not quite like OAuth. There is no "token" in Persona, we have keys and assertions.
The first step is for your browser to generate a public and secret keypair. Then you send the public key over to the identity provider to get it signed.
Once it's signed, you use your secret key (which never leaves your browser) to sign an assertion. The assertion contains your signed public key and an expiration, but it's also tied to an audience (i.e. the URL of the site you're logging into). That's what you send to the site you're trying to log into.
So if that site tries to impersonate you on a different website using the assertion you just gave it, it won't work because it can't change the audience that's inside the assertion (that would break the signature on the assertion). If the audience doesn't match, no other site will accept it.
Of course if a site steals your secret key from localStorage, then it's game over. However if you find a way to do this, then you've got yourself a browser 0-day :)