The most important thing to be looking at here is phosphate. Even if you have a barely detectable level, that is still enough to fuel an algae problem. Nitrate is also a factor, but generally phosphate is the critical limiting factor if you want to choke out nusiance algae. Also, keep in mind that regular hobbiest test kits generally don't have the precision to accurately look at the super low phosphate levels that we are going for on reef tanks. If the test gives a clear reading, you have a LOT of phosphate. If it gives even a hint of a reading, it's still a problem. (don't expect TI staff to be all that knowledgable about this stuff, they have a few informed staff, but also many who don't have a clue).
As far as cutting light, it may work to some degree, but if the nutrients are still there, and they will be, you are 100% sure to have the algae come back. The only exception to this is that sometimes you can light starve dinos and cause them to crash and not come back, but I don't think anyone can explain why. Standard green film, cyanobacteria, turfs, hair, and macro algaes will all come back if the nutrients are present.
When you do test or have someone test your water, be sure to also check the make up water you're using for phosphate and nitrate. If there is any of either in your make up water, you will have to do something about that. Even very small amounts will compound and build up because the fresh water evaporates out of saltwater but the nutrients don't evaporate so topping off will be constantly adding nutrients.