It is no longer necessary to get level 15 in a secondary class, as the cross-class system was replaced with role actions for combat classes.
To unlock a job, you need to
be at least level 30 in the associated class (thaumaturge for black mage),
complete all class quests for that class,
and complete the main scenario quest "Sylph Management" (at level 20, right after joining a Grand Company.)
After that, the quest to unlock the job should be available from the same NPC that offered the class quests. The job quest will lead you to a new NPC, who will offer all future quests for that job.