All currently known Season 4 Reloaded Obelisk locations for Unstable Rift.
Obelisks: Only 3 spawn in game at random and not all at same time or at beginning of game. Each Obelisk has an Ammo Mod symbol on the side of it which corresponds to the challenge of collecting zombie souls with that ammo mod. Once all three are done the Unstable Aether Rift will appear in game and marked on map. There is only one rift and it seems to spawn somewhat close to the vicinity where the last Obelisk was completed.
Unstable Rift: The Rift teleports you and your team to the Dark Aether on Al Bagra Island in Al Mazrah. It is wave based (5 phases) A Boss will spawn at the end of every phase, which will aslo spawn multiple of that boss during each proceeding phase.
Rewards: The rewards are ordinary loot rewards not exclusively "Ultra" or "Legendrary". Upon completion a Camo will be awarded as well as all Schematic Cooldowns reset.