Cyano isn't gonna hurt anything in almost all cases. It's just a phase, so try to relax while the tank gets itself sorted out.
Even if you let it pass without doing anything but siphoning excess cyano out along the way, it would take a while, but that's OK.
Assuming you've addressed the root of the problem, the best thing you can do is siphon it out if it gets heavy....and wait.
I'm not positive that the bad RODI water is the whole story though...let's make sure that any waiting is worthwhile.
How old is the tank, BTW?
Are you doing anything to create the zero/near-zero nutrient environment? Overall that's likely to promote cyano....or worse.
Do you have any other algae growing around the tank? Anything green?
How is your CUC? What's in it so far? ..and do they seem to work on it at all?
Stop doing anything like GFO, extra bio-media, carbon dosing, etc.
You may even want to consider adding some N and P fertilizers to get things moving in the correct direction – thriving instead of starving.
Cyano is always going to have a PO4-source on the substrate, and it doesn't take a lot of PO4 to facilitate growth. It also seems to have superior abilities at acquiring nitrogen for growth, even when nitrates seem to be unavailable.
Those conditions will be favorable to ultra-competetive substrate algae and they will be harsh for things like corals which have a need for phosphate, but have no direct access to the substrate.