I'm guessing it's the other way around:

THM > WHM
CON > BLM

As all class skills will be re-evaluated, our best bet is to go by the names and general concepts of the classes:

Conjurer: One who summons. This is a class heavily focused on elemental power, so BLM seems to be the natural outgrowth.

Thaumaturge: A performer of miracles or magic feats - often associated with healing. FFXIV put a life-death/astral-umbral twist on Thaumaturgery, but people tend to only focus on the death side of it.
Just that "Thaumaturge" is actually called "Master of Curses" in the Japanese version.
Doesn't sound like a WHM to me.