Couple quick things:
- Kat doesn't ask. She tells people to do things, gives orders, and punishments when people don't do what she says.
- Doing something like that in front of an audience, even a small one, means it wasn't private.
- Regardless of the incentive, that should have been a red flag, especially that early into his time at the club.
Telling him to get his dick out in front of strangers should have been seen as unreasonable at that point. What he's been told is that he's there to make sure the prospective carnations are safe and taken care of. What does that have to do with him getting his dick out in front of them? Nothing. It's just part of the power trip for Kat; she gets off on making people feel humiliated and uncomfortable.
At that point, Edwin should have asked for a clear definition of what he would be expected to do while working at the club. He's supposed to be an intelligent med student, yet he goes into this whole situation without ever getting his expected role clearly defined, or with concessions beyond "if you don't like it you can leave".
Basically that whole scene is there to give the reader an introduction into Kat's personality, and the tamest of what kind of content they can expect should they choose to continue.
It's a preview. Testing the waters to see how uncomfortable Kat makes you, and to see if you are okay with Edwin simply accepting the situation in which he finds himself.
If not, you may have trouble going forward, and find it hard to enjoy what's coming. Or, you may decide to continue with the ambition of getting back at Kat for being a sadistic malicious bitch, hoping to be a buffer between her and the carnations, and searching for an opportunity to take her down (or out).
