Did I do the right thing putting small stones under my deck?
Your downspout extension may be installed incorrectly. It appears that the black pipe coming out of the hill is not sloped properly and is causing water to pool inside of the pipe.

Since the pipe is not draining properly, organic debris such as leaves will clog the pipe and render it inoperable. Since water takes the path of least resistance, it will back up and then come out of the bottom of your downspout instead of out the extension.

The stones are not doing very much, and they are mostly decorative. Many people put stone, or some other kind of ground cover under their decks because it prevents weeds and grass from growing.

If you want to keep the stone there, I would recommend removing the plastic tarp from underneath it and replacing it with landscaping fabric. The fabric will allow water to drain through, and prevent weeds from growing. That way, you would be able to reduce the amount of maintenance in that area.