Unless you compensate. Receiveing a button press means the button was pressed <latency> ago. Rewind simulation to that moment, apply input to game state, replay

Unless you compensate. Receiveing a button press means the button was pressed <latency> ago. Rewind simulation to that moment, apply input to game state, replay to current moment, send result. Of course, single-player games don't usually do this, because it's very complicated.