The Terran, when a Mobilise order is placed, may move his base to another friendly/empty zone of the planet.

Is this limited to the owning player's Mobilize order, or can the Terran move his base when an enemy faction declares Mobilization on the active planet ?

It's the base owner who must execute a Mobilize order. And he can move it to a friendly area only. Note that movement is possible only before a battle is started.