In order for the Rebels to reveal their base, the Empire needs to send ground units in the system where the hidden base is located. Do the Empire ground units need to be the only ground units in the system? or if there are other Rebels ground units in the system, does the hidden base get revealed as well or not?
You're conflating two different processes. If the Empire sends ground units to the system containing the hidden base, the Rebels MUST reveal it, whether the Rebels also have ground units on the map in that system or not.
They MAY reveal it at the start of a Rebel action.