The main rotor behaves nicely in autorotation, no magic there.
At issue is the lack of a tail rotor. The coax uses differential collective pitch to adjust the torque balance and create yaw control. Want to yaw in one direction? Just increase the collective to one rotor, and decrease it on the other. This upsets the torque balance, and makes the aircraft yaw, while holding the total lift constant. Works great in powered flight, but in auto, there is no torque driving the main rotor, so little effect from differential collective.
That is why coax helos have big rudders, in auto, the rudders do the yaw control work.