This has nothing to do with manually shutting off the engine....
Try this:
Put yourself in a Blackhawk on the desert island and put a shilka on the map. The Shilka will shoot at you and more likely than not, your engine will die. Now, if you're flying around at 1000 altitude, it's far easier to properly autorotate, but if you're down in the weeds as choppers normally fly, you start to fall like a rock and don't have enough time to get this working properly - it takes a second or two before they start generating enough lift to lower you safely.
Maybe I'm not being clear about this, but this is supposed to save your ass when you're flying around in a chopper and are being shot down. It's easy to start descending and THEN shut off the engine (like what you said you did), but that's not the point at all.
In my experience you do need the warning, because by the time you hear the engine winding down, it's too late if you're at low altitude.