RE: when should drop away rest drop?
I'm with Tfox, the rest should be timed so it drops just before the fletchings reach it. Normally this means it will rise just as you are coming to full draw. If your rest comes up half way through your draw cycle it is timed way too early.
Having your rest drop immediately could cause the front of your arrow to drop with the rest because there is not enough momentum yet to keep it going in a straight line. This could cause slight inconsistencies that would effect your accuracy, especially at longer ranges or with fixed broad heads. It would also make tuning a nightmare.
Normally if you follow the directions that come with the rest you will have pretty good results.
A properly set up drop a way rest is not a cure for anything. The only thing they do is let you shoot a fletching that would not otherwise go through a prong or other type of fixed rest without contact. Truth be known a properly set up prong rest is probably more forgiving than most drop aways on the market. They are just hard to get fletching clearance with the new skinny carbon arrows, stiffer vanes and a hard offset or helical fletches. Using feathers and a light spring tension on a prong rest would give you the same results you would get with drop a way rest.
My opinions anyway.
Paul