According to the wiki, treasure chests determine their loot table at the time when the chest is interacted with via the player or hopper. However, in exploring ancient cities, the loot appears to be fixed upon generation not on interaction.

For example, if you go to a stronghold and find a chest, save the game before opening. If you copy the world multiple times, each time you open the chest it may have different loot because the loot is determined upon interaction (which seems to be the expected behavior).

However, if you go to an ancient city and do this same thing (copy the world before opening the chest), the chest will have the exact same loot always (which implies that the loot is determined and fixed upon generation rather than at the moment a player interacts with the chest).