Water accumulating on the side of our house
Start keeping a log or diary of all communications regarding this project. Record every phone call, letter, and visit. Write down who and when, and what you said and what they said.
Call the original contractor first. Tell him this is not satisfactory and he needs to fix it. If he won't come when the weather has been wet, you can demonstrate standing water with your garden hose.
Naturally he will be reluctant to devote more time and money to your needs. He may try to tell you that this standing water is no problem. Do not accept this. You will probably need iron-hard sales resistance. Maybe you will be lucky and your original contractor is honorable and wants to preserve his reputation.
If the original contractor absolutely will not fix this then tell him you will hire somebody else to fix it and send him the bill. Then hire somebody else to fix it and send the original contractor a bill. If it comes to this, you should ask over on Legal SE how to present the bill to the original contractor.