[i]I would instead speculate (from Hans Werner above) cyano grows when phosphates are spiked from foods and nitrates are limited.The carbon source will remove both phosphate and nitrates. Here is how I succeeded in removing cyano.
Blue-Green algae are well known to bloom in freshwater tanks when growth of vascular plants is nitrate limited. The issue you are seeing is tank is nitrate limited, not phosphate limited. I suspect the same is true in reef tanks.
I use Tropic Marin Pro with BRS 3 part recipe with an algae turf scrubber that is heavily cropped with high flow through. I went through a period of a cyano bloom for several months, however carbon source was DOC from Turf Scrubber not Actif. They were leached sugars and starches.
1) To reduce it I first created calcium as supersaturated condition. Kalk naturally does this but with 3 part raised caclium greater than 420 and carefully left kH 7-8. This will accelerate coraline algae.
2) Iron Gluconate to feed algae turf scrubber.
3) Microbe Lift Special Blend 20/cc per 180 gallons per day. Use of mineral flocculant is options.
4) Reduce feeding to every other day of only heavily rinsed frozen foods.
5) Wait 3-4 months. Yes thats how long it took. I have almost no algae and will increase feeding again now.
I would not add Iron if you don't have a large ATS that needs it. I discontinued after ATS growth slowed with it. Red turf algae also faded. I only have volonia as nussiance now. I had stubborn cyano that was on rocks not sand bed. It was also red turf mixed in.