It might sound odd, but our hands are supposed to exit through the golf ball as we make our follow-through. That term just refers to the path you need to maintain with your arms and hands to keep your swing on-plane.
To develop a feel for this important movement, you can use a pool noodle and watch yourself rotate in the mirror. Cut the noodle to size and add a slit to the end so you can insert a club, creating a T shape. Spread your arms apart and hold the club at both ends so it’s sitting perpendicular from your chest and, with the noodle anchored there, get into your normal swing posture. Turn your hips and watch yourself as your hands stay on-plane throughout the swing motion.