Hi, I played the game again recently and I'm already able to start the new event (I didn't though).
I think you'll be able to do it if you finished the Full Moon event with all the parts (except Caleb) and I think you need to have at least 1 heart with him.
For me, I have the option when I go to Sawmill to "Skip Time (Logan's Event)" after done those things.
Maybe you must have some progress on the Between Worlds event too, since I think the new event it's related to the Misty Abiss.