Decisions, decisions...

[Niwashi]

... since Thaumaturge is the White Mage's Tertiary class.

Actually it's an Arcanist. CNJ 30, ACN 15.

I think you mixed up secondary and tertiary there.

Primary class: Must be level 30 to unlock the job. All skills and traits from the class apply to the job. All XP gained with the job applies to the class.
Secondary class: Must be level 15 to unlock job. Certain individual skills can be cross-classed to be available to the job.
Tertiary class: Not required to unlock the job. Certain individual skills can be cross-classed to be available to the job.

Conjurer is the White Mage's primary class.
Arcanist is the White Mage's secondary class.
Thaumaturge is the White Mage's tertiary class.

[vanityobscene]

...

My mistake!