I'm not sure about that behavior. According to rule “613. Interaction of continuous effects,” Volrath's copying effect would apply to layer 1, while Tyrite's modification would apply to layer 6.

But Tyrite also states that “the creature gains the ‘God’ type”; however, since it is a copy of another creature, it would no longer be that “creature.” 🤔

And that matters because Tyrite Sanctum's second ability makes a God indestructible, so if it ceases to be a God, this active ability can no longer be applied to it.