When Volcano uses Explosive Eruption, it deals damage both via destroying its Presence and the Innate Power. Does Badlands apply twice?

When Volcano uses Explosive Eruption, it deals damage both via destroying its Presence and the Innate Power. Does Badlands apply twice?

No, because the damage from destroying its Presence isn't a separate action.
The Special Rule says, "When your Presence is destroyed...", which means the damage is done as part of whatever action destroyed your Presence.
(If it were instead a triggered action, it would say "After your Presence is destroyed".)