The evaporation of water, even at room temperature, actually is a simplified form of distillation. The water vapor that escapes the moist towel and finds its way to the tobacco below will be quite pure. However, there may be, and from your description of your water, there likely are more volatile, smelly chemicals in your tap water that may be getting into your tobacco. Personally, I always use tap water, but the water that flows from our faucets is some of the best water available. (Blessings to our water company!) My rule of thumb is simply this: if yo wouldn't drink it happily, don't use it on your tobacco. If the water is smelly, you can always boil it first, which will drive off the volatiles and give you a cleaner tasting/smelling water, or. Certainly, any dissolved minerals and salts will stay behind, never reaching escape velocity. As an example, if you leave a dish of salt water out to dry, the water will disappear, but the salt will be left behind. If you put a glass plate over a bowl of salt water, and taste the condensate, it'll be pure water. The same thing is true of the minerals in the water; they're not going to find its way into the tobacco unless you apply the water directly, which is one of the reasons I recommended my wet towel method in the first place.
All that notwithstanding, the more probable explanation is that if the tobacco affected you in the way you described, it's far more likely the tobacco itself than the water you used to rehydrate it, and there's just a fundamental disagreement between the tobacco and your own body chemistry. It happens. Since your experiences were with two different tobacco blends, as well as two different water supplies, there's no way to isolate which was the source of your problems. In order to derive any meaningful data, you'd have to repeat the informal experiment in reverse. But, given the unpleasantness of the result, I can certainly understand any reluctance to do so...
It's often tempting to draw conclusions based on incomplete data, but we have to be particularly careful when doing so. This is precisely what the antis do when presenting their "facts" regarding tobacco use.
-glp