>>Has it yet been determined whether or not spirit damaging spells will have to use TM as per physically damaging spells?

Short answer: No, it has not been determined.

Long answer: As long as spirit depletion can be fatal, a spirit-depleting spell will need TM. The ultimate fate of this system is still up in the air, though. At the moment we're only looking at Spell versus Spirit spells that don't directly screw with an individual's spirit health.

-Armifer
"It is no longer possible to escape men. Farewell to the monsters, farewell to the saints. Farewell to pride. All that is left is men."
- Jean-Paul Sartre