Stay away from the ‘Aliases’ tab. You don’t use it to configure virtual hosts.
First, create two directories one for each domain you want to host. I name my directories the same as the web domain they are hosting. For example, in your case, call the directories ‘mydomain.com’ and ‘otherdomain.com’ (using your real domain names of course.)
Now in the Web configuration section of Server Admin select settings and click on the ‘+’ button to add your websites. You’ll be adding two, one for each domain you want to host. Under ‘Host Name’ each should have the domain name they are representing, ‘mydomain.com’ and ‘otherdomain.com’. The ‘IP Address’ and ‘Port’ will of course be the same for both. Under ‘Web Folder’ for each domain you are going to point each to the two different directories you created for each domain. Restart the web service and all should be working.