If your head/neck is 'tucked' there shouldnt be a problem turning the head to either side, up or down. That naturally doesnt mean there wont be difficulty doing this. I cant really help you any more - I know there are exercises you could do if you have stiffness there. There's a very active forum related to the posture method
try combining it with this:
imagine there's a string pulling you upwards, stretching your backbone, separating the vertebrae. That might make it easier to move the head while keeping better neck posture. Some of the following chapters in the book deal with learning how to 'lock' this stretched posture so it's not a constant effort
. It's a nice feeling if you're able to really sit straight without that effort
It does take time for the body to change it's ways of course.