I shut down the motor, clip the fuel line, and throw it on the shelf.

It doesn't tilt left, it translates (slides) to the left, it needs right cyclic to make it stay put in a hover and will lean a bit to the right depending on the wind direction and velocity.
Its from the tail rotor blowing the helicopter sideways. They all do it, even the full scale helis. The name for it is translating tendency.