You can get some starter Pokémon in different Poké Balls. You can catch Charmeleon, Braixen, Ivysaur, Quilladin, Wartortle and Frogadier with any Poké Ball in the Friend Safari in XY. Those Poké Balls can then be bred down onto their offspring (except the Master Ball).
In Sun/Moon you can catch Chikorita, Totodile, Cyndaquil, Emboar, Samurott and Seprerior in any Poké Ball through Island Scan. These Poké Balls can also be bred down.
Some starter Pokémon distributed in events will be in Cherish Balls.
Primarina does not fit any of these categories. As of now there is no way to catch or breed a Primarina in a Dive Ball. The one you encountered is certainly hacked or edited.