I've had a lot of boys at this stage. He's not doing anything wrong at this point.
At this stage, he should be practicing both sides over a mat. Actually, his cartwheel would probably be easier if he were doing it off a panel mat.
He should not be worrying about a proper lunge in, cartwheel, land in a lunge. Side cartwheel is the basic. The lunge complicates thing with the 1/4 turn in and out. KISS.
The side cartwheel will be more difficult for those kids with poor shoulder and straddle flexibility and this might be a reason to focus on the front to back cartwheel. It still will go around the side until they get their shoulders open and legs more than 90 degrees towards 120 degrees. Some of this is because of the biomechanics and levers during inversion.
At this stage, it's all about the star cartwheel starting in an X over a mat or on the edge of the mat. They practice both sides.
1. one hand on each side of the end of panel mat. practice hopping from side to side over panel mat or a cone if they are placing hands at the edge of a mat (this way you can get 2 gymnasts on one panel mat).
2. hopping over one leg at a time. one leg then the other. they need to learn how to do this.
3. then they place their hands on the mat with the legs sort of in a lunge and hop over one leg at a time.
http://drillsandskills.com/article/10