My sons have a pulling off the ball problem. We think opposite field all the time but as soon as we swing hard in a game situation we pull off. The only thing that seems to help is to concentrate on starting the bat with the hands and not the upper body but to do that they both seem to push more with the top hand than what your literature calls for. We don’t roll over until after contact but we seem to generate a little more bat speed and barrell direction if we concentrate on the top hand. My guess would be that we were pulling with the lower arm and really getting nothing out of the top hand. We are confused about the role of the top hand. Without it our bats seem lazy and without direction. With it we wonder if we’re doing things incorrectly but we get better results.
As long as the top hand is not rolling too soon, it is ok to think, be more aggressive with the top had as long as the top hand is staying in the proper position and getting through the ball. If the kids are staying inside and through the ball you are ok.
What hitters mentally say to themselves is different depending on the hitter, if your sons seem to get their hands going better when they think top hand, then this is probably getting their hands going.
As far as pulling off the ball, make sure their effort level is not too high, hitters with a high effort level tend to pull of of the ball more often. They should feel like they have something let with their body when the complete their swing, also, if they are staying on balance throughout the swing, then their effort level is ok. Their effort level in batting practice and drills should be the same as their game swings, once this starts happening they will become more consistence.