If your RO is giving you 0 TDS already, DI might not help all that much. DI is necessary/unnecessary depending on your source water quality.
And water is not the only possible source of nutrients: could be the food you are using, or could be something dying in the tank that you can't see (things inside the live rock, for instance).
If you don't any photosynthetic animals, I would cut back on the light, and siphon as much of the red stuff as you can whenever you do water changes (if its cyano, it should siphon right off the rocks/sand quite easily with a medium sized siphon hose).
How old is your tank? If its relatively new, then this could just be the usual bloom that happens a few months in, and will clear up with basic husbandry and export pretty quickly without the need for any drastic measures.