Posts 2 and 3 hint at this: a certain amount of the "shrinkage" of the rubber happens when you roll the rubber onto the blade to make sure no air pockets form. Some rubbers are more stretchy than others, so, some stretch more during that process than others.
Does the factory tuning cause some of the shrinkage? I don't know. That may be the case. But if you roll the rubber onto the blade face, that definitely causes most ESN rubbers to stretch. In my experience, when I placed the rubber down from handle to tip without rolling onto the part of the rubber that had not been pressed into the blade yet, and just pressed straight down on the parts of the rubber already in contact with the glue, I did not get shrinkage. So I am not really sure.
One thing to examine: if the shrinkage is mostly from the tip and not from the sides: that is most likely from the rubber being stretched while being put on. If the total width, at the widest part of the rubber is also narrower than it was when you cut, then that means it is very likely to be from the rubber shrinking as a result of the dissipation of the factory tuning.
In the long run, I personally would not worry about it since you shouldn't be contacting the ball with the edge of the blade and if there was edge tape on the blade you probably would not even see it.
But, that is me and since it appears you would rather not have it, one method I have heard about is putting edge tape on the edge of the blade that is the thickness of the blade (no overhang, tape just on the edge of the blade: the edge tape cut to the thickness of the blade or like edge tape used to be in the 80s and 90s). Then when you put the rubber on to cut, you will be cutting about 1mm larger than the size of the blade face. If the rubber shrinks more than that, you could make edge tape 2 layers so you have a slightly bigger overhang for when the rubber shrinks.