My tap water does the same thing, and I change directly from the tap with water conditioner. I have been doing this for quite some time and haven't had any problems.
If you age your water the chlorine will dissipate and p.h will stabilize which is obviously better, I'm just too lazy to fill up all of those buckets I guess. No secret really, just a p.h test kit and sodium bicarbonate (up)or sodium biphosphate(down).