Organics have nutritient elements inside, however the decomposition process is what attracts algae spores because they are more capable than the plants of extracting these elements. Ammonia in NH3/NH4 from isn't an organic substance. But yes, ammonia is preferred by plants and algae as a nitrogen source. They utilise it better than any other nitrogen source and when plants or filters aren't capable of clearing that on time, algae will appear. The most common in relation to this is green water algae and diatoms. Tanks high in organics are not healthy for the fish themselves. There's a line one shouldn't cross, hence we do water changes,clean filters and siphon when applicable to reduce the levels of organics.
In the OP's scenario, if it is cyanobacteria, it could be related to lack of flow on the substrate, or also commonly associated with lack of nitrates if the tank is planted. A blackout for 3 days may do the job to get rid of it because cyanobacteria is light sensitive.
