When phosphates are 1ppm or higher, algae is likely to grow. Ideal is 0.05ppm.
Other things that cause an increase of phosphates (and algae) are. uneaten food, especially flake food that uses phosphate as a preservative. Plant decay, dying algae, fish waste, dead fish, aquarium salts, KH & pH buffers and of course tap water can all contribute to algae growth.
You might want to test your tap water for phosphates before using ferts thou. But, PO4 test kits only test for inorganic phosphates, so it's always a guess as to actually how high phosphates really are. The "presense" of any algae type is a "red flag" warning that your phosphates and or silicates are climbing. Sometimes large water changes only make an algal problem worse is because some water companies use phosphates in their water to protect the pipes. FWIW, the only real world answer to controling algae seems to be a phosphae absorber chemical like API Phos-Zorb, or similar.
Also, algae is a real hog for O2, so you may want to use some sort of aeration. And as far as light is concerned, from what I know already, a dimmer amount of light seems to grow "brown algae" or diatoms. Green algae goes nuts with too much light, especially light in the bluish spectrum. But again, it's the slow build-up of phosphates that will set the algae growing.
And since high levels of phosphates are harmless to fish is probably the reason not many test for it. Good water quailty also means low phosphate levels. In other words, plants like nitrates and algae like phosphates and organics. We really need to test and control / limit all three.
Hope this gives a more complete picture.