It emulates a ritual effect that persists on the body and extends to all weapons they employ, similar to the Celestial equivalent of Elemental Aura High Magic. To that end, since it is emulating a ritual effect, I believe you can use High Magic Earth Aura while Spirit Stored in a Golem.
Edit to add: Besides, if someone has enough Celestial and Earth magic (formal) to have both a High Magic Spirit Store and High Magic Earth Aura I would say they have earned that ability. That person sacrificed a lot by investing so heavily in dual-school casting, so reaping the High Magic rewards from both schools seems totally legit, to me.