Why do jet nozzles close at different rates? After recently seeing the trailer for Top Gun 2, I was reminded of something that I always wondered about: why do the nozzles of some jet aircraft seem to close at different rates? 

Sure, it's likely that both engines of the aircraft won't spool up at the same rates, but what about the nozzles? Are the nozzles dependent on the engine power output (which would then answer this question), or are they independently controlled? If so, what causes them to close/open at different rates?

Here's an example from the Top Gun 2 trailer:
The nozzle position is automatically adjusted according to the current engine state to maintain optimal exit flow conditions at the end of the nozzle.

The difference in nozzle actuation you are referring to is caused by a slight difference in activation time of the afterburner between the engines.

Please see the following Aviation Stack Exchange question and answer(s) for more information on the purpose of the nozzle:
Why are adjustable area jet engine nozzles mostly limited to military use?