I think Alexander fell into line about what Jadzia had explained about the race, that Klingons are as diversified a race as any other. While we mostly only see the warrior type ones, because they are the Empires form of military. We've never really seen many other Klingons that aren't. There are Klingon doctors, lawyers, chefs, artists, etc. Are they all aggressive? Even as a child Alexander was never aggressive but rather passive. It didn't surprise me in the least that he might grow up into that type of young adult.
Besides, how do we not know that what he experiences in the war isn't what changes him into the future one we saw in TNG? Seeing death and war first hand changes people, sometimes drastically.