By default, if you access your webmail using the main cPanel account (cPanel -> Webmail), the Horde webmail client is configured to display all the other email accounts that you have created from your cPanel -> Email accounts.

The option is configurable and you can disable/enable it from your Horde Webmail Client -> Options -> Edit options for: -> Mail -> Server and Folder Information -> Use IMAP folder subscriptions? -> Enabled. When you enable the "Use IMAP folder subscriptions" option the additional email folders will disappear from the main cPanel account.

If you want to keep all email communication private you should enable the above mentioned feature. However, if you need quick access to all email accounts you can keep the option disabled and use the main cPanel account to check all email addresses at once.