You can bind jQuery Mobile's virtual events, or bind standard JavaScript events to the input or textarea, like change, focus, blur, etc.:
$( ".selector" ).bind( "change", function(event, ui) { ... });
The text input plugin has the following custom events:
create
This event is fired when the input is created. You can bind custom logic to it like this:
$( ".selector" ).textinput({ create: function(event, ui) { ... } });