Jack made sure to administer the punishment on Arthur in such a way that he would not get out of bed for a long period of time. He had broken several of his bones, made sure that he would no longer go looking for girls like a randy he goat. In other words, he had, he had made sure that he faced the same thing that Collins faced when he tried forcing himself on Celine.
As for Johnathan, since Jack wasn't killing Arthur, to him, it didn't matter what happened to Arthur at all. Even if Arthur had died, he wouldn't have cared. It was just that he didn't want the matters concerning his death to be linked to him.
In other words, he didn't want his grandfather to blame him that he was the one that was responsible of the death of his cousin. Although he wasn't the one that would have killed him directly, he would have done that indirectly.
