I see I'm not the only one that personifies my audio gear. However, i usually keep it to myself so people don't think I'm crazy! Just sayin'!
This is a common issue with auto on/off systems. If you would like this feature, you can probably play with the gain to get it working. The objective is to increase the incoming signal so the amps sensor responds to it, so what you do is turn up the volume at your PS4 (and decrease the gain using the knobs on the amp so it isn't too loud).
That might not be convenient if you use headphones and want to leave the PS4/software volume at a specific level.
PS: I am not familiar with the PS4 so made some basic assumptions about how it is setup. Apologies if I got something wrong.