New South Wales
I'm a little confused about the food tile, does it move up the Nile river every time someone produces in general? Or does it only move up the Nile river if someone produces on the province with the food tile on it already?
The second one. It’s not explicitly stated in the rules but is implied by the explanation of what happens when the token is in AEGYPTUS INFERIOR:
It is located in AEGYPTUS INFERIOR and someone produces there (emphasis added) the “food” bonus market is placed in KUSH again etc.