you can only do this if the surface of the treadmill is an inertial reference frame. ie. a person running at constant speed vs a person on a treadmill at constant speed is functionally equivalent.
However, the moment you want to stop or change speed this no longer works - in the real world your body needs to accelerate, while on the treadmill the treadmill accelerates and your body does not. This is because the ground remains an inertial reference frame during the acceleration, while the treadmill surface does not.
Once you jumped off, you switched your frame of reference to the ground of the earth.
Keep your reference on the surface of the treadmill, and you'll see you've experienced negative acceleration.
This is why you always get an "extra boost" when you come off the escalator.