Coffee and tap water reaction - results in gray tint
The tap water might be slightly hard.  Hard water has a high content of minerals such as calcium or magnesium which makes the water more alkaline. Alkaline water will draw tannin out of the coffee much quicker than pure water.

Filtering the water with something like activated carbon filter then an ion exchange filter will lower the mineral content, thus lowering the pH. With a lower pH the dissolution of tannin will be slower.

Slowing the dissolution of tannin relative to more soluble portions like caffeine is part of the reason for steeping tea and coffee for only a limited amount of time.  More steep time, or more alkalinity in the steeping solution,  releases more tannin.  More tannin makes the coffee more anti-nutritional, more bitter, and it darkens the color.