I would guess your water is extremely hard and that the minerals in the water (alkaline, desert?) are either scavenging emulsion as it dries, leaving a "pimple" of emulsion in the center of the water marks or simply depositing minerals in the center of the drying spot.
Can you locate a water report for your area to see what the PH and dissolved solid levels might be?
Being that you can use distilled water and not have the problem, why not continue using that? Even filtered water would be better IF you have PH and dissolved solids problems with your tap water.
I lived in Odessa, Texas for several years and the Caliche in the soil made the water as hard as diamonds. People who used evaporative coolers in their homes had to scoop out the solids from the coolers and replace the water pads once a year.
Try regular filtered water.