$.ajax()
is jQuery, not jQuery Mobile, and has nothing to do with jQuery Mobile
pages.
Cordova proxies Ajax requests, fooling the browser into thinking
they are local.
jQuery Mobile still knows they are cross-domain, by examining the
URL. So, you have to tell JQM to allow cross-domain requests. JQM
defaults to not allowing them, in order to avoid unintended script injection.
JQM doesn't know nor care that you are using Cordova.
Yes, you have to white-list your domain.