Assuming everything was by the book, and to code, you should be fine. But it doesn’t hurt to talk to the neighbor about their concerns, to alleviate the concerns.

When we built our granny flat we made sure every t was crossed and i dotted. Because we were within the rules, it did not go to neighbor approval.

My husband also went and talked to the neighbors on either side, below us, and across the street to let them know what was going on. Kind of preventive damage control.

One of the neighbors below expressed concern about the roof/building pad creating more runoff water flowing into his yard. We showed him the grading and drainage plans (with basins and pumps that capture the water and pump it away from his house.)

When all was complete, we had a party and invited all the neighbors to see the finished project. The same neighbor said it was so much nicer than he feared, and was completely satisfied. He was able to inspect the storm water pump system up close and personal.

So… manage your neighbors concerns. Show him that you’re not impacting him.
If it’s a wooden deck – the water will still drain between the planks and be absorbed by the dirt below the deck. If it is a solid surface deck – then you probably do have to capture and redirect the storm runoff.