First off: I would like to see someone try repeating this with a factory module for comparison.
If I read this right, I reckon this means that something is not getting initialised properly in hardware with a rapid startup. The slow startup gives sufficient time.
Encoded RDS data is streamed to the DSP on the empeg, where it is recovered and decoded into useful info. The data stream itself is picked up by the tuner and passed, unprocessed, to the DSP.
If the empeg is started in AUX, then the motor is started after a delay and this makes RDS apparently work correctly, whereas an instant start screws up RDS, then either the control PIC in the tuner is not being given time to setup the tuner properly due to some race condition, or the DSP in the empeg is at fault due to some timing issue.
In either case, it will take some serious detective work on the hardware to investigate this.
I suspect you are out of luck if you are looking for this to be solved: however, if your start method is repeatable with all PCATS and RIO tuner units, you wil have made some big friends on this board