Runing view Cookies should show you these same cookies being returned by the AJAX call
If the lists don't match, try reloading this page, it sets a test cookie, but we can't see it on the PHP side until the client returns it on a test.
array(1) {
["PHPSESSID"]=>
string(26) "1kf678fg0vu8be46l2brchmrt6"
}