I loaded my save (warrior) before entering the warrior's guild, and tried with new characters (mage and survivor). Since it is apparently not random, my first thought was that it could be determined by character class or the type of attack used against the instructor.
As far as I can tell, if you have at least 2 points in Augment Defense and have a higher level of Augment Defense than Augment Damage, the game will give you a level of Augment Defense for beating the instructor. Other than that, you get a level of Augment Damage.
Note: If you have Augment Damaged maxed, you do not get a skill level reward for beating the instructor, even if Augment Defense can be raised.
