Some particularly bad power supplies can cause this - If +5Vs goes out of regulation on the low side or have excessive ripple, sometimes this will show up also on the PS ON signal, and might make the PS switch on by itself. Most PCs will spin the fans etc but not otherwise "wake up" just by applying full power to them without also intentional actions from bios/software, but maybe the applied power could in turn make such actions
I've had that happen to me before with dodgy externally powered USB hubs. Sometimes it would affect the 5v rail enough to trigger the motherboard to boot up.