It is all server side, so if you have two sections one that says "show if logged in" and one for "show if not logged in" it would seem impossible that both would not appear on a particular device, since that code and determination is made on the server and I can't imagine how the device would matter.
Maybe the fact that it displays or doesn't has nothing to do with the show if at all, but something to do with the actual HTML displayed.
If you create a copy of the page and remove the show if server code does it display on this particular iPad?