This depends on the specific splitter.
Standard Training Cables: Often, these are "live" for both microphones, meaning both users can be heard.
Switch/Mute Boxes: Many professional training splitters come with a switch box that allows the supervisor to mute their own microphone (listening only) or activate it to join the conversation.
Simple Y-Cables: Some basic splitters may only support one active microphone at a time to prevent signal interference.