If you search for your addon domain in Google, at times it may show as:
To avoid this, create a redirect so that access attempts to the specific directory are redirected to the full URL of the add-on domain. A redirect could be setup via cPanel to accomplish this; via cPanel, under the Domains section, simply click on Redirects to get started.
1./ Log in to cPanel
2./ Go to the Domains Section and Redirects
3./ Add a redirect for the addon domain path to the actual addon domain URL.
4./ Click Add.
Alternatively, you can also create a robots.txt file with the following:
User-agent: * Disallow: /addondomain.com