I think the confusion is in the formula section where you give the following example:
Lets see how this works in a brewing session. Assume a recipe with 10 lb. of grain, and that you need to collect 7 gal. of pre boil wort. A mash ration of 1.25 qt./lb. would require 12.5 qt. or 3.125 gal. of strike water. Based on an absorption of .1 gal./lb., the mash would absorb 1 gal. of water so wed get 2.125 gal. of water from the mash. Since we want to collect 3.5 gal. (or 50% of the boil volume), after the mash is complete wed add 1.375 gal. (5.5 qt.) of water to mash tun before the first runoff. Stir the additional water in, let it sit for a few minutes, then vorlauf until clear and start your runoff. After the runoff, we add 3.5 gal. of batch sparge water. Stir it in well, then vorlauf and runoff as before. These two runoffs will give us our pre boil volume of 7 gal. of sweet wort.
Since you are adding water twice after mashing, it sounds like a double batch sparge rather than a single sparge. The first time I read it I did not do so carefully and thought you were saying sparge twice.