Why do jet nozzles close at different rates?
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?