The best explanation for the observation that the balloon appears to move backward relative to the car when the car starts moving forward is:
The car moves forward, while inertia keeps the balloon in place.
This statement accurately describes the effect of inertia on the balloon. As the car accelerates forward, the balloon, due to inertia, tends to remain in its original position (which is effectively still relative to the ground) and appears to move backward in relation to the car.