I googled, and found a lot of stuff suggesting that Pyrrhura conures start puberty between 1 and 2 years, but I can't find when it typically ends. However, based on what I know about other species, the rule of thumb seems to be that puberty seems to last roughly as long as it took to hit puberty, maybe a little longer. So hopefully, he'll be out of it by age four.
The only bird I ever got young enough to go through puberty was one lovebird. He hit it about a year after I got him (from a pet shop, unfortunately, so not sure of his age), lasted about a year and a half. During that period, he became extremely aggressive towards almost all the other birds in the house (except my sun conure, whom he decided was his mate); once it passed, he mellowed out towards all of the birds who had been in the house when he went through puberty. (The female lovebird, we got later, and he never warmed towards her.)