Nichole,
If the water is standing near the edge where the asphalt is a little higher, it is possible to heat that edge with a propane torch and tamp it down with a heavy metal narrow hand held tamp. I don't see any short term damage being caused by a little standing water, however it would be wise to broom it off especially in the winter. I realize those are specialty tools which most homeowners won't have, but you could request the contractor to try this relatively simple solution. Feel free to contact me if you have any other questions.
Bronson
864 871 2647
