Krampus doesn't change progression through the trade order system at all, aside from giving you more of a reason to do them.
To get credit for a guaranteed Krampus drop, you must complete three trade orders without using a moongate. Orders run through moongates do not count towards the ~25 runs needed to spawn him, nor towards a guaranteed Krampus drop. (Moongate use does not penalize progression, it just doesn't count for Krampus and you won't get the high-end order rewards from the destination city.)