I do believe what you've been told is correct. The state of charge in your battery will determine the start voltage when your alternator spins up.
The time taken for the voltage to rise depends on the power output of the alternator, and the size of your battery bank. If you have a good alternator controller then the voltage will rise to the set charge voltage for that particular type of battery. 14.4v, 14.8v or 15v. It should maintain this until the controller determines that the battery is charged, and then drop to float, 13.2v.
Remember though, it does depend on having a proper controller on the alternator, check this out.