Plus, it is a reasonably common science fiction trope for Earth natives to be referred to as Terrans - possibly because it has a little more gravitas than "Earthling". (Which tends to be used more as a derogatory term by aliens believing themselves to be superior.)
On the whole, I'd probably be inclined to use "Tyrian" as a native of the world, more specific names otherwise. Certainly, though, there are some ambiguities, as "Tyrian" could be an inhabitant of the world or the continent, and "Canthan" could be an inhabitant of the continent or the nation. Possibly the same for Elona now that Palawa's conquered it under his banner, too.