game of thrones - How do the Unsullied prioritize their orders?

This is an example of the book explaining it better. Though there are differences between the show and the books they are based on, this scene is close enough that I can answer your question better because of what I read and the detail it went into that the show didn't have the time to.

The Unsullied are trained in a way to be mindless and abject of desire or care. They are given special narcotics which desensitize them to feeling physical pain or pleasure and are trained to obey any command they are given by breaking their spirits by having them kill a baby while the mother watches and by killing their puppy that they have raised. The symbol of their obedience is the whip that Daenerys receives from Kraznys. There is no other training given to the Unsullied they must obey whoever holds the whip and is proclaimed their master.

The problem with Kraznys and his people is that as slavers they assume that everyone needs their services and that no one would ever fight them because they make the Unsullied. Daenerys however is so sickened by what they have done and what they will continue to do that she buys the Unsullied because she is in need of an army and because she wants to end the practice of making them. All of the other slavers do have whips but they are not whips that symbolize control over the Unsullied. Think of the whip as a key. It doesn't matter to the Unsullied who has the key just that the are controlled by the owner of that particular key. Daenerys orders them to kill all of the slavers.