Nothing will happen as long as it doesnt rain before they get the shingles put on and even if it does the plywood resist swelling and warping better than OSB "oriented strand board" the ice damn keeps ice from forming under the bottom rows of shingles and forming widowmakers "icecicles" which may pose a safety hazard not laying tarpaper is less time consuming and more cost efficient and when your paying them as much as your paying them per hour the contractor's saving you money