A LFS that closed down not long ago in my area was selling top off water with a TDS of 101. ... that's 101ppm more then what it should have been. Basically, he was selling tap water. Make sure you test your LFS's water's TDS reading to make sure you are buying clean, pure, freshwater. Test it for ammonia if you can.
I don't think your lighting has anything to do with it. You're keeping your lights on an appropriate amount of time and not exceeding the maximums to start the light cycle off with...
If the algae is bryopsis, then you would have reoccuring algae in the same spots on a few various rocks. Phosphates are leaching out of the rocks and the algae is using the phosphate within the rock to grow... so it wouldn't be your water quality or your top off water quality or feeding or lighting that would be causing it. Usually, you can take the offending rocks and turn them over and put the algae in the dark. If that doesn't work, you can set a non-offending rock on top of it to smother it out. Bryopsis looks just a tad different from hair algae - to someone with a trained eye, it's pretty easy to distinguish between the two.
Are you making a mistake? I don't honestly know. There are many aquariums out there that DO use bioballs still - successfully and without algae. There's a problem somewhere in your system - your top off water, your feeding habits, your husbandry habits... something, somewhere is causing a build up of nitrate and phosphate that is being used by the hair algae (maybe) to grow. I don't think it really matters if you go ball-less.
What are you feeding and how much?