Note: You must visit the "Riding the Storm" level once before you are able to access the four subworlds.
In this video, I cover the initial visit to the "Riding the Storm" level of "Moody Clouds".
At the moment, there's nothing to do here but watch a short cutscene in order to unlock the four subworlds. We don't have nearly enough Electoons yet (and I've been collecting every last one of them), so obviously there's more to do before ending the game.
In case you're curious, even though you can can effectively complete the subworlds in any order, I intend to do them in the "proper" order. If you're not aware of what that is, it's starting from the subworld attached to "The Jibberish Jungle" and then working our way clockwise, just like we did for the regular worlds.