you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
That's a perfectly fair point - but becomes irrelevant once the engines have started pushing against the air!
If you sit the toy car/plane/whatever on the treadmill/conveyor belt/whatever,
and turn it on, the vehicle will move back with the treadmill, like you say.
Why? Because friction within the wheel bearings inhibits them from spinning up and allows the force on the wheel by the conveyor belt to be "transferred" to the entire aircraft.
This frictional force is very, very small, but clearly evident - on normal ground it may take more power to get an aircraft moving initially than just to taxi along once already moving. The engines, in providing slightly more power, have overcame the small force of friction within the wheel system, and allowed them to spin!
This is exactly what happens when the conveyor belt is moving and the engines are applying force in the opposite direction. The conveyor belt "tries" to move the aircraft backwards, but the only way it can do this is through the small amount of friction in the wheel bearings. The engines have already overcame this friction, as they would when taxying on normal ground, so the net effect is that the engines push the aircraft forwards relative to the air, whilst the conveyor belt simply spins the wheels faster than they normally would (as a component of both the forwards motion of the aircraft and the rotational point of the wheels, and the backwards motion of the conveyor belt).