I can confirm that the head movements are an integral part of classical waltz dancing, and for a very practical reason. Dancers spin around so much they can quickly feel very dizzy. The head turning, left, right, left, right, diminishes the dizziness.
I haven’t seen the show yet but the waltz is in my eyes the easiest ballroom dancing to learn, there’s only 1 set of steps to remember, and the head movements of course. Hope and Aiden may have been able to learn it in about 30 min top!