You must select stars 3-6 after completing stars 1 and 2 to spawn the owl.
Momentum is stored and reversed when you jump onto the owl, so try to land at the spot shown in the video and jump directly up without touching the analog stick.
Turn on the tree by holding right for a little bit before jumping out.
Alternatively, there's a strat (Madowl) involving speed conservation when jumping into the owl. Although it's generally not recommended, it saves about 2s over the traditional owl strat. See the video linked here: https://www.youtube.com/watch?v=3CIFQ3EEu_8
Owlless (Standard)
Select Star 1 to avoid tower lag and/or spawning the owl.
Beginner: No camera change, hold up-left for fence clip. Hold slightly up after landing on the spinning platform to do a slow turn.
Advanced: When implementing the quick turn on the island, it's highly recommended that you perform the camera changes (2 C-Rights and 1 C-Up) before rolling out on the island. This will give you more time to prepare for the quick turn and allow you to hold A before you land so you can begin the triple jump with a buffered kick.
