For the Jedi characters, at least, it kind of makes sense. In the general Star Wars canon (and explicitly stated in TOR1), the older you get, the harder it is to undergo Jedi training, so pretty much all apprentices are quite young.

It could also swing for Sith characters, but there is something of an implication for both the Sorc and the Warrior that the player characters were already pretty skilled with the Force, so they could have been Force-users for a long time before arriving on Korriban.

In the case of the Smuggler, and Bounty Hunter, it's easy to be flexible with the character's age since there isn't really a timeline on those careers, and either could have started young, or gotten into the profession well into their life.

The only place the young age estimation becomes a tough sell is in the Trooper and Agent characters. The Trooper is experienced and well-proven enough to get placed in Havoc Squad, which, according to their reputation, is probably about as difficult as getting an officer commission, and would take a little time, barring extremely exceptional circumstances. A field agent for Imperial Intelligence is roughly on-par with an Imperial Military officer in terms of expertise and experience, if not actual direct authority. Imperial Intelligence doesn't just let any young Imperial hopeful stroll in the door and sign up. There's probably pretty rigorous training involved, as well as the background need to prove that the Agent is loyal enough to the Empire to serve with Imperial Intelligence.