If the voice doesn't match the account owner, it doesn't give out any personal info. If you use somebody else's Assistant, you can only get general search results or media payback, typically.
Honestly while Google is far ahead of Amazon here, they still recognize like 9 out of 10 voices as the "owner". Just not 10 out of 10 like Alexa does, which is utterly useless and will happily recognize a cat meowing as its trigger and allow it to unlock the front door. >.>
I have a couple of phones in use. 1 never answers which is fine as I have a display too, but the other answers every time I can do that if you unlock your device first.