The delay classing you speak of applies to IJN (and the delay is to lvl 80-ish not 40). It may also be other nations but AA gunner classing is nation specific so there is no universal rule.

KM you should class on time (see also KM forums).

its related to the gain of ability,

japanese aa gunners (dual purpose gunners) get a small reload ability reduction by classing them to DP gunners, so by classing them later they gain more reload every lvl. (at later lvl's, they accumulated enough reload ability to class them into AA, previous BB's also dont have to many T slots to use AA anyways)

you can look this up by looking at the sailor info on the NF site. folowing the table from;
km sailor > arm sailor (+8)> AA gunner (+2)> 1st aa gunner (+0) > chief AA (+0)
IJN sailor > arm sailor (+7)> AA gunner (-5)> DP gunner (+0) >chief DP gunner (+0)

you can see the base growth rate for each type you class them to, if you click the sailor type in the table.
i noted them behind the types to point them out;

the ijn ones have a -5 reload reduction when classed to AA, which you dont want to happen since theres no boost afterwards anymore. for KM you get a +2 boost when classing as soon as possible, so its a boost to your stats if you class them right from the start.

Since AA gunning means faster gunnery, the AA sailor needs all the reload base growth it can get (not AAW, because AAW is the automatic anti-air fire coming from your ship). Often, classing to higher AA levels kills off some of the reload base growth.

IJN

Lvl12 Arm Sailor +7 Acc +7 Rel +8 AAW << this is good, adds to base growth
Lvl20 AA Gunner -5 Acc -5 Rel +4 AAW << bad, kills the base growth of Accuracy and Reload

Remember, the AAW stat is ineffective for higher level planes, so its not sought after. Its always the Reload stat (and Accuracy to some degree) base growth you're interested in because as your reload piles up at later levels, you'll see the marked increase in rate of fire.

Theres alot of Arm Sailor class AA gun choices, but of course you'll have to work with slower gun reload speeds at first. Usually I'd choose the hardest hitting one for the specific AA ship space requirements, and I work my way up on the slow AA reload. Classing to AA at lvl80 or even higher levels (lvl100!) is what I usually hear from others, but of course some guys just class it earlier.

One of the alternative uses of this kind of sailor, when not AAing, is as a hedgehog user, so it has alot of uses as it reaches those higher levels.