The inertia of the spools determines how fast they will accelerate for any given increase in torque on the turbines.
The surge margin determines how much of a torque increase can be applied without the compressors stalling/surging.
The turbine temperature limits determine how much extra fuel can be added without damaging the turbines.
The FADEC limits the rate of increase in fuel flow to prevent surge/stall of the compressors and overheating of the turbines.
They are all in it together.