It's not normal, but she may have her reasons (less work on her part / maybe she thinks it shows you're more serious about seeing her).

As someone who has rented their space before, I'd also want to talk to the Domme since she's in charge of the session. If A ProDomme didn't want to rent from me directly and is doing it through their sub I'd honestly assume the worst (bad history in the community, bad renting reviews, doesn't want to screen, ulterior motives, is irresponsible, etc). I'd probably wind up denying you both the request or screening you both twice as hard.