I have no doubt in the world that your mystery algae is Cyano Bacteria, also known as 'Red Slime.' This is hard to get rid of, especially when not using RO/DI water to start a new system this algae, along with green hair to be very common during a systems maturation. It will typically last about a month or two. A couple ways for control on this is to remove phosphates via a phosphate sponge, or use a competing algae. Caluerpa works well in this regard. Most fish or Inverts wont eat this stuff. Water changes are highly recommended, RO/DI water!
Likely you have high phosphates in the aquarium. You might want to think about soon getting a 'Clean up crew' This would consist of things like 10 Astreas, 5 Trochus, and a couple Cerith/Baha (from Sea of Cortez), 1 Fighting Conch, a couple Nassarius Snails, and _cerith _snails are all good part of a clean up crew. Some tiger tail cucumbers are also good, 1 will be enough, and these arent poisonous, like the other cucks.
PH =)