Hi GPS,
Disclaimer: I am not a chemist (yet). My info is from reading on labels, books, and other forums. You should always confirm what I say since I am not an expert.
What I mean by fallout or precipitate is when minerals bond and make a solid that the plant can't use. You will notice this by finding what looks like dirt (like from iron) or scale (calcium deposits) on the inside of the reservoir. Some micronutrients don't waste time doing this. If you start with poor quality water, precipitation begins as the nutes hit it. So, you should adjust prior. If you are using a good
nutrient, adjusting prior should render adjusting afterward a moot point. If you are using rain water or RO, it is likely you have a good pH to begin with. Tap water is often as high as 8.3 from what I've read on other forums. Mine is a little lower, but not much. That is way too high for many micronutrients. You are certainly correct that you want to use as few adjustments as possible, but the point of that is that you are supposed to start with good quality water in the first place so you won't have to adjust too often.
Your medium can further cause you to have to adjust, of course. For example, coco coir often reduces pH. You should test the water off of coco after you expand it. The water from GH Coco tested around 4 for me and had an EC of 3.0. I was shocked. So, yeah, you might have to adjust before and after. But adjusting only after won't fix the problems you caused by failing to adjust before. It only prevents them from getting worse.
I don't believe that letting the chlorine gas off will affect your pH that much, but I could be wrong. Tap pH is usually high due to the dissolved solids if I remember correctly. I was recommending the wait based on allowing the pH to stabilize since it is likely the starting pH was pretty high. However, it is supposedly good to let the chlorine gas off just to protect the tender roots. Especially new ones.
GH recommends that you adjust prior and then check again an hour after mixing the nutes. Of course, they sell the adjusters.