Sleeping on your tummy means that your neck has to be fully rotated to breathe (unless you have a hole in your bed!).
This means that your joints are in a closed packed position all night which will raise tension within the joints in the side of the neck that leaves you vulnerable to neck stiffness in the morning. Over years this can cause problems.
Good pillows and a good sleeping posture helps a good night sleep but also helps to have a pain and stiffness free neck.