When two transistors connected which one is on and which one is in cutoff from given circuit condition?
Look at this circuit carefully and realize each transistor is being used in emitter follower mode.  However, as you say, at most one of them is on at a time.

To decide whether a transistor is on or off, look at the voltage across its B-E junction.

Hint: Remove any transistor that is off from the circuit, then analyze.