Booker says that in the "falling stage," the hero is "underdeveloped" and in the shadow of something "dark" that may "spring entirely from within the hero's own personality." In other words, there's no evil spell being cast over Holden – he's doing this all to himself. By writing off everyone around him as "phony bastards," Holden renders impossible the chance for him to ever connect with a person, essentially prohibiting his own happiness.
In this stage, the "dark" power seems to have receded. Holden thinks that by leaving Pencey, he can leave behind the phonies and embrace a more genuine, open life.
A more genuine open life? Fat chance. Holden feels lonely almost immediately, essentially imprisoned by his own judgmental tendencies. It looks as though he's reaching out to others (like the three women in the Lavender Room), but he's still judging them internally and making impossible a real connection with them (like the three women in the Lavender Room, who he deems to be moronic and pathetic).
Even if you think the Mr. Antolini incident wasn't sexual, it still works as the Nightmare Stage. Look at it this way: if Mr. Antolini is coming on to Holden, then the one person (outside his family) he was really starting to connect to – the one person who gave back in their relationship, instead of just taking – turned out to be doing so for selfish and questionable ends (questionable because Holden was a former student and is still a young guy). On the other hand, if Holden only imagined the friendly gesture as a sexual come-on, then this is just a continuation (and in fact, a powerful resurgence) of the same "dark power" that has a hold on Holden from the start. Holden is imprisoning himself from Mr. Antolini's friendly advances because of his own judgmental and suspicious mind.
Booker literally says the Rebirth Stage consists of the hero being freed by a young woman or child. But how exactly does Phoebe free Holden? Well, she is the only person in the novel to have a genuine and compassionate conversation with our protagonist. When he cries, she puts her arm around his shoulder. She lends him her money. She covers for him when their parents get home. But most important is the carousel scene. Phoebe gives Holden his hunting cap back when it starts to rain, showing that she cares about him and his individuality. And she helps him realize that the process of growing up and "losing innocence" doesn't have to be a dark and scary one. Kids have to grab for the gold ring, Holden concludes, even though it means they might fall off their horse and bruise themselves. Does he escape from the "dark power" of judgment and alienation? We're not sure. But we can be certain from this final scene that he learned from these escapades in the city. And so did we.