To oversimplify somewhat inaccurately for illustration:
In a pushover, the rotor pushes the airframe down and makes you light in the seat.
In a rapidly-entered autorotation, the airframe pulls the rotor down, making you light in the seat until the autorotative airflow is established.
However, as long as you go down-right-aft (or left in those helis), you will not get the "decouple" or the rolling moment due to T/R thrust, so no mast bumping (or droop-stop pounding) is likely.