I did not realise that Coffman produced a system similar to the pneumatic starters that the British used on a lot of engines and the Russians still use.
Obviously, like the Brit and Russian systems, there must be a distributor valve that directs the airflow to which ever cylinder has just passed top dead centre. I would presume that it also, like those systems, distributes the air to more than one cylinder in sequence until the pressure dissipates.