Board Thread:Legitimate Canon Questions/@comment-212.11.105.251-20180808001836/@comment-4091815-20180809174949

Lydia didn't transform from her bite. Banshee's are immune to werewolf and other supernatural issues (Kanima venom etc ).

Jackson's transformation was explained a couple of times in Season 2 - "Instead of becoming a werewolf, Jackson transformed into a snake. We are led to believe that this shape reflected his inner turmoil and outward behavior."

Kate's was pretty much the same deal, bad on the inside made her different on the outside.