I believe that during engine start, when the START SWITCH is placed in ground, a signal is sent to the APU FCU to increase up to a maximum of 110%. APU rpm will adjust to maintain a schedule PSI for duct pressure until its maximum operating temperature has been reached. Then the APU FCU will reduce fuel to maintain the APU within its operating limits.
Doesn’t the EEC monitor the engine and send signals to the HMFCU to provide a uniform rise in EGT which is designed to avoid hot starts?