Search - Do you use default zone URL in search content source?

Using default zone URL in search content source, it will be automatically convert to the relative URL on the search result (e.g. if a user access search "keyword" via http://projects.ssw.com.au/search, the result will be like http://projects.ssw.com.au/search/keyword).

While another user access search center via https://projects.ssw.com.au/search, the result will be https://projects.ssw.com.au/search/keyword.