The 301/302/303 redirect is performed by the XmlHttpRequest handler of browsers, not jQuery. This does not explain why you do not have a callback. But this may explain why the redirect is not verified on the ajax side.
, 302 , , 301 303. 303- . , GET ( ).
, ( , ).
302, , , , : ajax. HTML-, ( ), ( JSON?), json-, , , URL- ..