I just looked at the scene. If you watch carefully, you'll see that in each instance Mr. Miyagi is acting defensively. The other person makes the first move, and he counters it. So he didn't jump anybody.
That said, the general rule is that a person has the same rights in defending someone else as they would have in defending themselves. So, if Mr. Miyagi had gone in just cleaned house to drive off the attackers, that would be fine without any regard to their ages.
Where he could get in trouble would be excessive force, like trying to injure someone further after they'd been subdued, or pursuing someone after they had fled.