Indonesia is part of Asia because it lies on the same continental shelf as mainland Asia. In just the same way, the British Isles are part of continental Europe because they lie on the same continental shelf. Here's a wikipedia definition... https://en.wikipedia.org/wiki/Boundaries_between_the_continents_of_Earth .

The island in question is a very popular destination for Aussies and Brits but perhaps not for Americans. The name of the island exists in a song title in a Rogers and Hammerstein movie.