Setting up screen time limits for child question

I've gone through the steps to set up screen time limits (for some reason I've had to do this several times to get them to save) for a child on our family. My question is this: Do we need to log out and log back in with their ID to make sure the screen time limits work? How does Apple know it's them using it and not us if we don't? And if we do log in with their ID, that means we lose connectivity to all of the app sign ons? (like Libby or Audiobook)?