My best guess is maybe it means all tigers are under her control as if they're her human servants but without the metaphysical life-binding?

Then hell to the no, on Anita being Master of Tigers.

I support some random person being Master of Tigers. Does it have to be a vampire? It shouldn't. If so, it should be some young fledgling vampire of the rotting vampire line who has no fucking clue what's going on, and just happens to stumble into this whole thing. Her name can be Nova or something, and Lucy can bring her over, I don't even care. Anything to keep it from Anita.