This is actually very easy but might be interesting for someone anyhow (and I post it here as a reminder for myself). You can use Postman (https://chrome.google.com/webstore/detail/postman/fhbjgbiflinjbdggehcddcbncdddomop?hl=de) to send requests to your ProcessWire installation and test request answers. The problem is that $config->ajax will always return FALSE. To make the $config->ajax work properly you just need to add this key-value-pair to your requests: key: X-Requested