I must admit I was wondering much the same thing myself, in spite of not being a great follower of lore. Alexander would surely be some teenage brat rather than an elder politician type, unless Lucian adopted someone much older than himself.
Then again Bioshock Infinite was kinda like that: precocious teenager sets up awesome flying steampunk city and promptly ages several decades because space magic happened.
Then again II I'm just snarky because I haven't had enough sleep. Or cheese.