I'm having the exact same issue. Sent emails bounce with the message "TLS Negotiation failed, the certificate doesn't match the host".
Worked fine 2 days ago.
I can receive emails correctly with the same address.
If you want to use secure mail, you need to use the server hostname in the settings rather then your own domain, your domain would not have a valid matching certificate, as it would attempt to use the servers certificate.
By "hostname", she is referencing the name of your server. Your server has an SSL certificate, but that certificate is only valid for x13.x10hosting.com. It is not valid for mail.(domain).com. Please use x13.x10hosting.com and let us know if that works.