Google searches on an add-on domain

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I have what cPanel refers to as an add-on domain  (e.g.
 It points to a directory (addon) in my main domain (say
 This saves the expense of a new IP address. Browsers can access the
content of either by going directly to or
by going to

When Google crawls, including the directory addon,
presumably the content of the directory addon is cached under the URI  Is this correct?

If so, when users Google a term that is in the content of, they are referred to this site, but also to  Is that correct?

If so, how can I prevent referrals to from occuring?

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