Question on domain redirection

[mileagedriver]

Dear fellow warriors...I have a domain www.aaa.com redirect and I create backlinks for this domain and suddenly if the domain is changed to United States and Canada BBB Consumer and Business Reviews, Reports, Ratings, Complaints and Accredited Business Listings and google started to show United States and Canada BBB Consumer and Business Reviews, Reports, Ratings, Complaints and Accredited Business Listings at search results but when clicked redirect to www.aaa.com redirect. Is this bad? In such case, I must create backlinks for aaa or bbb ? please help. I think it is pretty basic but can't find the real(hidden) truth behind this.