I assume your RO
unit is the style that has the carbon cartridge before the RO
membrane? (this is the most common type)
The most common RO
membrane is sensitive to chlorine, so the chlorine is filtered out before the water goes through the membrane, and the resulting water is completely unprotected against microbes.
How long has it been since you changed your filter cartridges? This mossy stuff must be living off of some nutrients remaining in the water, unless there's nutrient rich dust falling in the open top.
This may sound crazy, but if it was me, I'd set up the reservoir as a freshwater planted aquarium. If plants and algae are competing for nutrients remaining in the water, then more harmful things won't get as much of a chance to grow. A less eccentric approach would be to sterilize the whole system, get new cartridges, and put a tight lid on the reservoir.