The P360 should share a common ground with the IPAC. Also if you use a transformer, I would be careful to insure the voltage is very close to the IPAC. Many 5V transformers can fluctuate.
Furthermore, the P360's outputs are normally high at 5V until the stick is moved. This means that 5 volts is normally flowing from the P360 into the IPAC on the Up, Down, Left and Right pins.
Does anyone know how much tolerance the IPAC has for voltage fluctuations on its inputs?