Billing in the credits is contractually negotiated by the representatives of each actor. I suspect the billing order is also indicative of how much each actor is paid for their services, although that is not necessarily so (there is also, of course, the actors at the end receiving "and" or "with" credit, and so on, who are probably paid more than the actors preceding this special billing).
It certainly has nothing to do with screen time and is often not tied to appearance (and in this series main title billing hasn't been tied to appearance).
You are correct, the only exception I have seen is Game of Thrones that only puts people on the credits that are in the particular episode. I just found it odd that 2 of the 3 'top billed' stars were not in the premier episode. But then again, there are a lot of storylines.