I agree with Alice being vulnerable and I feel that if we say she's the Isekai'd is her then she'll be put into a lot of danger that she can't handle, then if we say we don't know it may lead them to assume it's Alice anyway, so I think our best option is to say that we're the Isekai'd.
Moon Door!
I fancy helping stop a tyrant if it leads to the underground world as I suspect. Also there's the joke to make about Alice going underground so it's like Alice in Wonderland XD