You should use "mail.domain.ee" in the User Editor. However, that value is not related to the current problem. If your Outlook is not able to resolve mail.domain.ee, the problem is not in Xeams. Problem is that your DNS server (the one Outlook is using) is not able to resolve the name.

I recommend you post your actual host name on the forum. If you don't feel comfortable doing that, send us an email instead with your real domain name. We can run some tests from our end to confirm if the values are entered correctly in your DNS server.