Often they prefer you to transit their overhead, and I have been asked to do so (irritating on my CPL skills test!). They are usually very helpful, remember military controllers don't have anyone concerned about how much the service costs! They are also grateful for your call, which is not mandatory (though I would strongly advise it!) and helps them plan their own traffic for greater safety.
If they ask you to do something you are not happy with, make another request of them. They may be able to be more acomodating or to give you help - for example if they ask you to change route they may be able to tell you where you are when you leave their zone.