I am confused, was this house freshly painted or painted a year ago?
If the stain is in the paint, there is nothing you can do unless you are a painter also.
Looks like they did not kill the mold/mildew before painting and it is coming through the paint. I have seen this happen a lot of times.
The additives they put into the paint don't always work when there is mold/mildew there on the surface and not taken care of before painting.
The house wash mix will not soak through the paint to address the problem, it needs to be taken care of by a painter unless you also paint.