I cant give you one answer to fill all, but I will assist with pSX.
first of all you have to set the controller to Dual Shock or Anolog+rumble on the controller settings and check the Rumble check box. ( Don't use the Analog+rumble Type setting, use the Dualshock one. Regardless of whether you actually have a DualShock pad or not )
Second, not all adapters work for pSx
also, some games just give troubles others dont. If a game doesn't officially support rumble/vibration, there's no way a pSx will provide it.
I think the same goes for epsxe