One of the ideas that goes along with the "ring finger lead" concept is to keep your thumb on the 1:00 side, if the top of the ball is considered to be 12:00 on the clock.
Along with these, if you're doing them correctly, you will also keep keeping the flat part of your wrist facing towards the pins, as will the inside of your elbow.
When your hand is more on the side of the ball, it's as if your brain doesn't believe the ball will hook and is trying to help it by turning it. When this happens, you're ALMOST always turning the ball early, which hurts rather than helps.
"Standing at the foul line" drills practicing this can help you get the feel of what you want. Also, it might be easier to do this at home, rolling the ball into some pillows on the floor, with you, kneeling on your right knee with your left (slide) foot on the floor next to the left knee. (Reverse if left handed). At home, you can watch your hand as you release, getting a feel for what's happening, without worrying about people staring at you or your interfering with anyone else.