This is due to the fact that South Island is an ever-moving island, with the Chaos Emeralds existing within the distortions it creates.
The Japanese manual for Sonic the Hedgehog (1991) describes South Island as having no set location as it is constantly in motion. This supernatural movement causes "distortions" that then house the Chaos Emeralds, with this most likely referring to the Special Stages in which they are found in-game.