An Addon domain is a new, unique website hosted in a new folder on your account.
When you create an Addon domain, 3 things happen:
1. a folder is created in the 'public_html' directory
2. a subdomain is created for the main domain and attached to the new folder
3. the new domain name is associated with the subdomain
As such, if your main domain was 'abc.com' and you attached the Addon domain '123.com' to the folder '123', the following routes would be true:
abc.com/123
123.abc.com
123.com
They would all access the same directory and, thus, the same website. However, the functionality of 123.com holds true such that when a visitor goes to 123.com, all they know is 123.com -- there is no evidence that they are being routed through 123.abc.com behind the scenes, and everything functions normally.
This all happens automatically when an Addon domain is attached to an account -- no 'fix' required.
There is, however, also a method in which you can disable the '123.abc.com' route from accessing the site without disturbing the '123.com' route.