The contractor working at your house, I assume, knew what the work was and quoted a price to you. They didn't pick the house name off a list, and were then told the work to be done, and the price they would be paid for it.

If they aren’t ironed out then you made a foolish decision. I would never let the contractor decide the materials, how things look, the color, etc.

In your case the specifics should be ironed out for your safety. In the Uber example, you are the rider and you agreed to pay to arrive somewhere but let them decide the route.. and you pay for time/distance.