Pulling the hands in doesn't matter much to me. Ted Williams pulled his hands in to load his scap, but it was also part of a hitch. J's weight shift occurs at the wrong time, which makes his swing two-pieced. He shifts, then swings. Stride is controlled by staying on the back side and only once the swing launches does the weight shift into the front leg, not onto it. Because he rushes onto his front side, it's difficult to get the barrel behind and through the ball on a slight upward plane.
Here's Mauer demonstrating more what I want to see. Of course, if you look at the back foot, it is weightless at a point in the swing. stylistically speaking, some players' rear foot would come forward or lift off the ground, etc.
And I want to be clear here. I know there is a lot more time to work on his swing and they are certainly looking at a mirror, so we will see what other changes they work on. Unlike some guys, he is willing to be coachable.