The Plex apps do not do any transcoding. It’s done by the server. I must have missed the description you gave on how it is working on the web clients.
Another issue some have with running the iOS client is that “http://plex.tv” is not being resolved correctly. I would suggest that you go through this checklist, with Item #2 (and DNS Rebinding) possibly being important in your case. Also, review the notes in the follow-up post regarding IPv6.
