Turn roundcube to a virtual host

I am running my mail server on a Ubuntu 14.04 box without any issue.
To check emails I have installed roundcube using the deb packages with aptitude. The program was installed to /usr/share/roundcube and set up a conf in conf-available this way:

# Those aliases do not work properly with several hosts on your apache server
# Uncomment them to use it or adapt them to your configuration
    Alias /roundcube/program/js/tiny_mce/ /usr/share/tinymce/www/
    Alias /roundcube /var/lib/roundcube

# Access to tinymce files
<Directory "/usr/share/tinymce/www/">
      Options Indexes MultiViews FollowSymLinks
      AllowOverride None
      <IfVersion >= 2.3>
        Require all granted
      </IfVersion>
      <IfVersion < 2.3>
        Order allow,deny
        Allow from all
      </IfVersion>
</Directory>

<Directory /var/lib/roundcube/>
  Options +FollowSymLinks
  # This is needed to parse /var/lib/roundcube/.htaccess. See its
  # content before setting AllowOverride to None.
  AllowOverride All
  <IfVersion >= 2.3>
    Require all granted
  </IfVersion>
  <IfVersion < 2.3>
    Order allow,deny
    Allow from all
  </IfVersion>
</Directory>

Now on every domain hosted on this server, if I add /roundcube at the end of the url, I see the roundcube login page. As far as I know this is set by the first two lines in the conf file. I am not so strong in Apache configuration to see what should I do after commenting them to set up roundcube to be reachable only with a domain like webmail.my_mail_server.com
This domain resolves correctly to my mail server. The issue is only on the apache side.
Thanks for the help!