When I want to move say a cultist from one region to another one, do I have to pay a cost to do it? Or does the cost only refer to the initial summoning?

It's my understanding that you have to pay the cost. Otherwise, Khorne would have an easy go of spinning his dial.

Yes, unless you use a card or something to move the figure you have to pay the cost, and for all intents and purposes moving a figure from your supply to a region is the same thing as moving a figure from one region to another.