Zero water? As in from the commercials on TV? Well, I personally struggle with their claim of 0 TDS
from a set of filters without something like a DI
resin involved to remove the remaining impurities that filters can't touch.
Though with that said, I'd say that water source is 10x better than tap water.
That said, algae still feeds off of light and nutrients in the water column. Can't live without one, so there are nutrients in there...most likely in the form of phosphates that are tough to detect on a hobby level. They would either come from the water source itself or simply aren't being exported from the system after being added from when you feed your tank.
The large water changes will get you in the right direction. Just remember that even a 50% water change will only cut the levels in half, not remove them totally. It will take a series of large water changes along with manual removal of the algae to solve this issue. It takes time, patience, and in the end some frustration.