How can there be parallax shifts in the "home" position as I rotate the sky? And then I realized that this is a promotional tool for the Online Star Registry,

How can there be parallax shifts in the "home" position as I rotate the sky? And then I realized that this is a promotional tool for the Online Star Registry, one of several novel sites which will "name" a star for you in exchange for money. It is not meant for scientific or educational purposes, so realism need not be foremost.