I am currently using ExtJS 3.3.1, I have not made the switch to 4 yet, but most likely when a new project will appear. Despite the source of Ext, I can tell you that they use JSONP to accomplish this task, this is the only way to make an AJAX cross-domain, because JavaScript must obey policies of the same origin .
Are you trying to execute a pure JS implementation of JSONP? Or are you already using the JS library?
Edit
According to our comments ... they make POST requests. This is not possible with JSONP. As far as I can tell, they use tricks iframe. This is the same trick used to download AJAX files in older browsers.
This link explains this in more detail.
, (iframe to, POST, upload file) Valum. ExtJS.