Setting csrf_regenerate as TRUE

First I'm asuming you are using jQuery

Your AJAX code should have a success and error handler for responses.
The controller/method that is called via the AJAX could respond with JSON output

Code:

$.ajax({
   type: "POST",
   dataType: "json",
   url: 'http://www.somewebsite.com/some-controller/some-method',
   data: theDataYouAreSending,
   success: function(data){
       // This is a success response
       csfrData = {};
       csfrData[data.csrfTokenName] = data.csrfTokenHash;
   },
   error: function(data) {
       // This is a error response
       csfrData = {};
       csfrData[data.csrfTokenName] = data.csrfTokenHash;
   }
});

In the called method you could do this

PHP Code:

$response = array('success'=>TRUE/FALSE);
$response['csrfTokenName'] = $this->security->get_csrf_token_name();
$response['csrfTokenHash'] = $this->security->get_csrf_hash();

header('Content-Type: application/json');
echo json_encode($response);
exit; 


The data argument in function(data) is an object containing what ever you added to the output