For one, he has already jumped the fence once, tackled, and "mouthed" a child. That's extremely concerning to me. As much as we may not like it, we own a breed that is often viewed by the public as dangerous and if that behavior happens again, it would be very simple for someone to sue you, call animal control, and pursue euthanasia for your "dangerous" dog. I don't want to be mean, I just want to make sure you understand the reality of that behavior now.
So after he jumped the fence and mouthed the boy, he now gets to see them run screaming away from him when he is in the backyard. This is not a good association and I would assume does not elicit a desirable response or association between your GSD and the kids. Get the yard behavior under control now. Don't let the screaming kids become a thing for him. If the neighbor kids come out, either bring your GSD in or engage him in training or play so good things happen around the kids.
It is good that he was in obedience class. Continue to work with him. I usually teach my GSD's to ignore children in general. In controlled situations, he does not have to be a "do not pet" type of dog, but it sounds like you need to put much more work into controlling his interaction with children. I would start off by stopping interaction between him and children for now. He lunged at a kid and then you let a five year old walk him around the track? Unless I've got the timeline wrong, that's not something I would ever, ever do. It's simply too much of a risk.
It's hard to know exactly what's going on without seeing it, but I would make a point of having space between him and children for the time being. Drill leave it's at a safe distance from children. Children should not be something that excites, scares, or worries him. They should be really below his attention. He should be focused on you. Drill greeting. When my dog greets someone, their butt is cemented to the ground and their mouth NEVER opens for mouthing or barking or they are removed.
It could be aggression, it could be puppy excitement, it could be that he jumped the fence because he thought it would be fun to chase the child and that child is now associated with rough play. In any case, it needs to stop now. And his interaction with other children needs to be monitored very strictly to make sure he does not decide any other children are alright to lunge at. Until he is bombproof with greeting and attention behaviors, I would not personally facilitate any interaction between him and any strange children. When it comes to kids, there is simply too much risk.