[The Owl House] How could Luz use her glyphs on the Titan Trapper island?

It was clearly stated that the small finger island they started at already didn't belong to the Boiling Isles Titan aka Papa Titan, and then they even got teleported to the other side of the world.

So even if that Titan there was also still somewhat alive and able to power magic, it should have required a different set of glyphs to use, just like the glyphs of King and his dad are different.

The only available source of Papa Titan's magic in a wide radius should've been... Hooty. Like, his bilesack, if he has one. But if proximity to that was enough to power the glyphs, Luz also should've been able to use them in the human realm, when all of her friends with their inherent magic were around.

Or is Papa Titan's magic just so damn strong that it covered the entire globe so long as he was still somewhat alive? But then it seems really weird that the same power that has so much range couldn't reach just a few meters beyond the open portal door when Luz briefly crossed into the human realm during her fight with Lilith.