Is it possible that we still receive message on our mail server that aren processed by MX Lab even after setting the the MX correctly?
Yes, this is possible. Spammers will not always follow the MX records and try to guess or to detect where emails can be delivered directly. Such attempts can sometimes be very easy by guessing a common name that is used for mail server, for example mail.yourdomain.com. In this case you can reconfigure your firewall or mail server to only allow incoming emails from the MX Lab Gateway.