While the choices may be arbitrary(ish) or story(ish) driven, I ran a bunch of chapter 4 dungeons yesterday and (while there were no relics) I got an inordinate amount of Dronei pets and no others while before the pets drops were more random. And if you look at the evolution of Dronei it requires - - - relics from the chapter 4 dungeon. It appears that each dungeon acquired one or multiple pets that are associated with said dungeon.
Would it be possible to add that pet association info to the rewards screen?