Well, even if we didn't get to SEE it, we do know that Alexander had to have changed off screen since he was promoted to Weapons Officer. On a Klingon ship there are only two ways to move up the latter.
One: Be exceptional at your job.
Two: Kill the guy that is your immediate superior and take his job.
I seriously doubt that Alexander would do the second option that soon after seeing him at DS9 but in either case, we do know that he became a "True Klingon" in one of those aspects.