Phosphates. This is at large the biggest cause of hair algae. The trouble with phosphates is that most aquarists check the parameter but because most test kits available are inaccurate they get false readings. Giving the impression that phosphates are at an acceptable level. The most reliable test kits to date are the Deltec phosphate test kit, but this is very expensive. The solution is very easy to solve. Use a phosphate adsorbing media such as rowaphos in direct flow in the aquarium. Using a inexpensive phosphate reactor for the media is much more effective and comes highly recommended. Either way ensure you change media every four to six weeks.
Water Movement. Water movement or circulation is very important, if not enough flow is available you will get "dead spots". Areas that have no circulation. Here is where detritus builds up causing high nitrates and phosphates, This is where your algae problem will start to grow and spread. The solution is either upgrade a current power-head or add additional movement through a second power-head.
Lighting duration. You will probably over look this since many corals need light to survive. But too long lighting duration and/or placement of aquarium near a window in the days sun will cause growth of algae. If you have no problems with phosphates or water movement i would recommend reducing lighting cycle and/or move aquarium, close a curtain to block sunlight during the day to see if algae growth reduces if an aquarium move is a massive task.
Total dissolved solids.TDS present in RO water or your saltwater mix will also contribute to algea. It is highly recommended to use water with zero TDS present. Always check, I have an inline meter that tells me as soon as it rises, when it increases I change the DI resin. You can read a little more into this in my Article TDS and how to get it to zero