Tadlock knows that no other form of justice will do for the Indians if the wagon train is being pursued by them out of vengeance, so he hangs Johnnie, for the safety of the traveling party, but to their outrage.
Tadlock realizes that any other form of punishment wouldn't be acceptable to the Indians if they are pursuing the wagon train in retaliation.  Therefore, he kills Johnnie to ensure the safety of the travelers, but this action causes outrage among them.