I've had new clutch type posi units do what your describing with regular non synthetic posi gear oil and the sperm whale additives whiney shruggy
Even making the out side wheel and tire jump and hop on tight turns shockdown
Continue to drive it after getting the pinion seal sealed up so it doesn't leak

Mr.Cab Racing and winning with Mopars since 1964. (Old F--t, Huh)