Henshin no Jouken
Conditions for Transformation

When members of the Sohma clan who are possessed by the spirits of the 12shi are hugged by members of the opposite sex, they transform into their animal form. Parents and family members are no exception. Having one's child that was just born transform the instant you hold them...... Momiji's mother was unable to overcome that shock and continued to reject him. However, hugging members of the opposite sex amongst the 12shi does not lead to any transformation.

Also it becomes more common to transform when the body becomes weak. The snake Ayame can't handle cold very well, such that if the termperature should fall too low, he accidentally transforms. Regardless of situation, given time, they will revert to normal, however, they can't control this themselves.