I personally don’t think it matters much between most balls, except the really cheap ones from Walmart (I forgot the brand).
I have a decent handicap and have been playing used balls I got from my instructor a few years ago. I played a few rounds with new ProV1’s that were gifted to me and my scores remained the same.
I doubt that’s why you hit the ball fat with this method. It’s more likely that you’re doing something else to compensate for the setup. Jim himself rotates when demonstrating his swing and rotation alone will not drop the club head.
I'm a mid handicapper. I love the feel of Pro V1, but when the ball lands on the green I typically get 6 feet of back roll. I don't like it. I now use Tour Soft balls and when they land on the green they usually stay no more than 3 feet from the ball mark, either a little in front or a little behind. I prefer this. Cheaper balls like Titleist Velocity hit the green and continue rolling forever.