Hi Joseph! It is always interesting to get unexpected results! However, i am very surprised that the testing company would say you are 'not a Williams'. Usually, all they do is show you the list of matches.
It may well be that the names Davies and Davis occur frequently on that list of matches. That is an interesting situation but not in itself conclusive that the Y-DNA belongs solely to the Davis/Davies family.
There are several possible scenarios that could result in what you are seeing.
One of those scenarios is that the Most Recent Common Ancestor between you and your Y-DNA matches predates fixed surnames. If your ancestry is Welsh, "the use of patronymic names continued up until the early 19th century in some rural areas". That would mean that, in the olden days, cousins whose dads were brothers David and William would have different last names: David's kids go by Davis, and William's kids go by Williams, even though the male cousins all have the Y-DNA of their grampa, David and William's father.
Since your family seems to have come to the New World in the 1600s or so, it is quite likely that this practice was still going on in Wales when they left. Over the next 200 years, men carrying that Y-DNA could have come to the New World and shifted over to the surname system instead of the patronymic system at any point, thus locking in a different surname.
That is one possible scenario. Another possibility is that the Davis/Davies crowd in your matches are actually a minority in the 'real world' even though they are a majority of the testers. (At this point in the use of Y-DNA, that could happen if a family gets gung-ho about testing and has lots of family members do it.) Out of a bigger population sample, there could have been more Williams than Davis/Davies on your list of shared matches, or another pattern altogether. How many shared Y-DNA matches do you have altogether? How are the others related to each other?
There are other scenarios that you would want to rule out, which could include undocumented adoptions and NPEs anywhere along your line or the Davis/Davies line.
Unfortunately, so far there are no other descendants of your progenitor who have Y-DNA tested and shared that info on WikiTree.
If it were me, I would hit this puzzle from two sides -- first, i would work backwards from yourself to see how far back the Y-DNA has stayed the same within your own family, and at the same time i would try to find at least two other male-line descendants of your progenitor to test. The DNA Descendants tool for your William Micajah Williams shows a few possible candidates still living whose tests, if they would participate, would possibly indicate how far back your own Y-DNA has been consistent in your family.
Let me know if this makes sense to you.