Have you completed the level 20 Main Story Quest called "Sylph-management"? Hunting log doesn't matter, but you have to have finished that quest, all Conjurer class quests (1, 5, 10, 15, 20, 25, 30), and have Arcanist to level 15. The level 30 quest to unlock White Mage is given by E-Sumi-Yan (the same guy who gives the Conjurer quests) once all of the requirements are met and you have finished the level 30 Conjurer quest from him.