Eventually, the reaction calmed down and I was able to proceed with the wall-cleaning. And it worked: The rubbing required was also significantly less than when I was going the soap-and-water route.
If you have water stains that extend across ceilings or run down walls, the cause is probably a leaky roof. Tracking down the leak is the hard part; the roof leak repair is usually pretty easy.
This way, engineers can figure out where the water needs to flow below ground in tunnels, on the surface in covered trenches or in pressurized pipes, or above ground on walls or arcades.