I beg to disagree!
While the description of the man's part is more or less accurate visually, he will be standing on his right toe only. He must not have weight on both toes, or the lady will be unable to complete the couple's turn as she dances her cross. It's important for the man to neither rush nor retard the lady as she finished her action.
"The first step must not be taken under her own hipline, but out of it."
I'm not sure if you are referring to the first step of the double reverse, or the first step of a following figure, but regardless, the lady always steps under her own body on the first step, because she moves her body not her foot. She must never step with her foot alone while leaving the body behind. Failure to maintain the body in vertical alignment over the foot when entering a heel turn will result in off balance posture and a forcibly faked heel turn.