DirectAdmin won't care. If DChub can be installed for a specific domain then it should be installed exactly the way the DChub instructions tell you to install it, using your domain's public_html folder as your DocumentRoot. If DChub works on subdomains you should set it up in the subdomain's Document Root. If you create the subdomain under DirectAdmin as a subdomain of your domain, that would be the directory with the same name as the subdomain. If you create the subdomain under DirectAdmin as it's own domain, that would be the domain's public_html directory.
Note that the public_html directory you see upon ftp login may NOT be your domain's public_html directory; it's generally under this path:
<USERNAME>/domains/<DOMAIN-NAME>/public_html
where <USERNAME> is replaced by your login name and <DOMAIN-NAME> is replaced by the full domain name not including the "www".
Note that I don't know anything about either DChub or Teamspeak; I have no idea how they run or where they need to load; the above instructions are quite generic.
Jeff