I've got that problem myself, but I bought a pump with a build-in sponge filter, which I clean every week.
Algae shouldn't grow in the dark. You sure it's all nicely covered?
Another thing is the pH. Algae don't like pH I think chips are better than mulch. There's less compaction.
The stones would work too, but you should mix it with equal parts of perlite/wood chips to retain water. I use a stone grit the size of kitty litter mixed with wood chips with great succes.

The whole point with hydroponics is to use a sterile medium. Are you using sterilized mulch or just ordinary mulch?

It's too easy to run into problems with algae and microbes without adding starter colonies in your media.

If you don't have some kind of filter (like a sock filter) for your pump inlet you'll want to get one asap, but unless you start with a perfectly clean system, and keep any kind of contaminate out, you're going to have a certain amount of microbial growth.