The motors did NOT stop during the "emergency only" CSC descent, they spun as required to maintain and not exceed, the maximum descent rate for the flight mode.
I think you will find that the "left stick down" i.e. the throttle fully closed is a method of stopping the motors if the drone has landed but not automatically stopped the motors.
The CSC position is both joysticks fully 'down'/towards-you and fully 'in'/towards-one-another OR both joysticks fully 'down'/towards-you and fully 'out'/away-from-one-another. These three positions are the same as those used with the P3Adv so you may have encountered them with the P3S. I found that the "left stick down" method is the better method of manually stopping the P3 motors when the P3 has landed, the CSC position made it possible for the drone to flip if there was wind, it isn't so important with the MUCH lower mini. As a rule I do not use automatic landing or take-off .