I have had horrid water where I live (think 700TDS) but if they add chloramines, which I suspect they do, it has not affected my tank after running the water through my RODI unit.
How large are these fish, and are they tangs? Tangs can have a higher bioload due to their high-fiber diet.
What exactly are your parameter numbers?
How warm is the tank? I'm not sure how accurate it is, but I've heard that warmer waters can encourage cyano growth.
Try adding a good-sized clump of macroalgae to the sump. If the problem really is high nutrient levels, the algae will help remove that to discourage the cyano.
Do you spray anything in that room or in the room you store your RODI or saltwater (air fresheners, body sprays, etc)? I've seen anecdotal evidence that these, even if not sprayed right next to the tank, can contaminate your tank and feed cyano.
Lastly, check your fresh-made RODI water with a TDS meter. It may be that your unit filters and/or membrane need replacing.