hi.
The brown/purple stuffs on top of the sand is cyanobacteria. There are many causes of cyano, and water can be one of them. However, before pointing to the distill water, may I ask you what do you add to the tank beside distill water? (e.g., fish food, phyto, chemical additives.. etc.) What is the bioload beside the corals? Do you test your nitr*?
Very often, a slight nitrate (very rare in distill water) can lead to massive cyano bloom.