I don't think the rule applies to children before they begin attending Hogwarts, and maybe children who never get to go to Hogwarts. After all, would they be putting children on trial when they unintentionally use magic like when Harry let loose the snake at the zoo, or when Nevill bounced after his fall? After all, a kid can't be expelled if he's not even in a school to be expelled from.
Bless the Beasts and the Children