OK, this is where it gets weird.
I've always been told to reduce string tension. Why? I never asked, to be honest. So, I did a Google search and this is what I found.
Most don't say to reduce or maintain string tension when making a trus rod adjustment. They're no help, but a few said to relieve string tension. But they don't say why. Why?
But if string tension is mentioned, they usually say to leave the string under normal string tension when making a truss rod adjustment. So, it appears you guys are repeating the same with the majority when string tension is mentioned during a rod adjustment.
OK, now this is what one site said about reducing or adding string tension before making an adjustment;
Caution!
Never adjust the neck under full string tension - always de-tune the strings first.
But notice, they don't say why. So, why, then? Meh.
I do know that no matter if there is string tension, or not, you should never adjust more than a quarter of a turn in one 24 hour period. This gives the neck ample time to settle in its new relief position.
OK, so string tension can be maintained when making a rod adjustment since nobody has experienced any problems so far since so many suggest to leave the string in full tension. If there were any problems, they would've shown up by now. But, since there are no problems showing up otherwise, I've never had a problem reducing string tension before making a rod adjustment, does it really matter if you loosen the strings first or not? I say, "No."
I've had success, and an easy time, with adjusting the neck relief with little to no string tension, so why should I change now? I notice the strings don't get in your way as much when making a rod adjustment when you loosen the string tension, so it is easier to do it that way. For me, at least. And, the neck relief moves the same amount with or without string tension because you are turning the dial only one quarter of a turn, anyway. So, I guess it's business as usually for me, like it's business as usual for you guys.
I guess this a case of "different strokes, for different folks."