Green algaes are mainly from excess nutrient and phosphate levels. It may be that the
PO4 is 0.15
ppm but when you initially added the new tap water to the system it was much higher and the algaes have since used it up for the most part. Have you tested the tap water directly to see what that level is? Keep in mind, foods will also add
PO4 to a certain degree.
Once these algaes are established, I have found that they will not always go away by themselves even after the fuel source is eliminated. It requires some manual removal on your part as well as natural animals that may help if you do not already have them. I find zebra hermits to be very beneficial with hair algaes and a variety of snails will deal with the film algae. Cerith, nerite, trochus, turbo and margarita to name a few.
In a 57 UKgal tank, a mixture of 30 or so should be a good start for that size tank. I would also suggest not using the tap water again.
RO water will be the best bet for top offs and water changes as you will not really know what metals and other unwanted minerals you are adding to the tank that may perpetuate the algae problem.
Which Red Sea skimmer do you have? The base model or the Pro model? It could also be part of the issue if not doing frequent enough water changes and the skimmer being to small, there would be elevated
DOC in the water that will feed the algae.
Cheers
Steve