How do player loyalty rewards work?

Does the game simply have to be on your trophy list or do you have to have the actual previous game saves? And do you get a higher reward for higher achievements, or is it one rewards that’s the same for everyone?

I got heads and skins for all pre-sequel characters for playing Bl1, Bl2, and a couple weapons and a shield for purchasing Tales from the Borderlands season pass. The rewards were located in the “shift” kiosk in pre-sequel in Concordia, where you redeem golden keys. My guess is you need a “shift” account, ( I could be wrong about that though.)

Also, I was on ps3 and transferred over to ps4, same console family, not sure if that affects anything either.

So the more BL games you played, the more you get? Or do you just need a shift acc showing you played at least one?