and yes your tank is really very young so give it time and start rowaphos or phosban as soon as you are able and it should help elminate what you have now and continued use will help eliminate future outbreaks.
I have two green chromis and I feed them brine shrim or flakes ~every other day. I target feed my corals brine shrimp once or twice per week, and I do a small dose of zooplex or phytoplex once per week (alternating weeks). So red algae is a cyanobacteria like the freshwater blue/gren algae? Also, how long does it take to cycle out of a maturing tank. Is it like another month or two, or like 6mo to a year?
You can probably cut down on the feeding, if you see that they aren't eating all of the frozen brine then try cutting the cube in half. Also phtoplex may be adding additional po4 into your system, which isn't helping the problem. IME I have found that phyto products have led to more algae growth, and had no visual effect on other organisms. The red algae should go away with time, but it might take different amounts of time for different people. It should go away in less than a month unless something continues to leach into your system.
Cut down on feeding which raise the nutrients, also cut back on photo period, siphon as much away as possible, increase flow in the areas it is accumulating, cut the phyto back or IMO get rid of it completely, I would switch to a frozen food that you can rinse before you feed as David said the flakes are loaded with phosphates. Also do more water changes. Are you sure this is Cyano? If this is the case the above will get rid of it.
However if you have a diatom bloom which is the browner stuff that looks like cyano, it is caused by high silicates in the water. More than likely is from the tank being so young but could also be coming from your RODI. Simple way is to test the RODI for Si and if you get a reading you know what the problem is. If you get no reading of Si than you know it is just from the tank being new nd will go away on its own.