In the case of the genny fault lights, the aircraft has electrical power applied, either from the GPU or the APU. So as far as the aircraft is concerned, its electrical system is energized but the gennys are not producing power, so it illuminates the fault lights.
(To confirm this, I will check to see next time I switch on the aircraft from cold if the genny lights illuminate with batteries only or when the AC system is powered. I don't think they come on with battery power only).
In the case of the hydraulics, there will be a non return valve between each (Green/Yellow) system and its ENG HYD pump. This is necessary because otherwise, if the Green or Yellow ENG HYD pump had failed, but the system was being pressurised by the other ENG HYD pump via the PTU, then the ENG HYD pressure switch would 'see' pressure but would not 'know' if that was from its own pump or another one, so it would not be able to tell if its own pump had failed. (The main purpose of the ENG pump non return valve is to prevent fluid loss if the ENG pump were to shatter or to suffer a seal failure).
If an ENG pump fails, but system pressure is maintained by other pumps and the PTU, the non return valve downstream of that ENG pump will close and the pressure switch - situated between the ENG HYD pump and its non return valve- will 'see' low pressure and operate the fault light.
What I can't work out is why Airbus would suppress the ENG HYD pump fault illumination when the engine is not operating.