Most of the Tisiphone inmates can be divided into three groups: werewolves, veela, and vampires. Perry can easily control the werewolves (he worked for the Werewolf Capture Unit for 20 years, of course) but he doesn't have that much experience with veela or vampires. He certainly doesn't want to end up seduced by a veela or 'make a blood donation' (to put it lightly) to a vampire.
So he's looking for some inmates to help him out with that. At Hogwarts, each House has 2 prefects, right? That's sort of what Perry is looking for. It' not really a formal situation with a title and special privileges, it's more of a 'I'll scratch your back, you scratch mine' situation. The two prefects would protect Perry from being manipulated/attacked by their species and in return... they would get power and whatever else they might want. Let's work out a deal.