How do I make my character pool soldiers follow their choosen class?
You can train a rookie soldier to a class of your choice in the Guerrilla Tactics building. If you acquire them as rookies and level them in battle, you're stuck with the semi-random class up.
"Chosen Class" for character pool options only applies when you gain the character as a veteran soldier (i.e. Black Market), and the character starts out at higher rank.