Most of the time nitrates come from the food you feed and the poop from the fish, if you have no way of processing nitrates in your tank then they will just continue to grow.
If you are feeding frozen foods then try to rinse them in RO water before you feed, that can help a lot. I only feed my reefs 3 times a week, but none of my fish need a lot of feedings and have plenty to graze on from the LR.
The only way to remove nitrates from a closed system is: water changes (and even these cannot really keep up with the nitrate build up at some point), a algae scrubber (a refugium with macro algae, as the algae grows you remove it and that removes the nitrates), or a DSB , the DSB processes the nitrates, LR also processes nitrates but not as well as the others.
As far as using RO water, there are a lot of other things in tap water other than nitrates that I wouldn't put in my tanks, but if it works for you then, you should be fine. Most cities do have nitrates in the water that is why it is one of the first questions asked when someone has a nitrate problem.