If you (manually) configured (the DNS of) our mail and the mail is not being send successfully, there is probably a record misconfigured or missing.
To find the cause of this problem you should look in the log files of your VPS. Generally speaking the command "tail -f /var/log/maillog" (Postfix) or "tail -f /var/log/exim_mainlog" (Exim) will give more information regarding the specific reason of not being able to send mail yet.
If the log shows a notification displaying "No valid 'x-transip-mail-auth' DNS record found for <hostname>. Please see https://www.transip.eu/question/110000764/ for more information.", then the required DNS-record can not be found by our mail service. To resolve this you should check if the required record has been successfully added to the (sub)domain you are trying to mail from. If the record is not present, please add this and try again later.