The reason Jeannie's entire family are magical when she frequently mentions growing up as a human is because the curse put on her when she refused to marry the blue djinn extended to her entire family. Jeannie2 was once a normal human girl who just wanted to dance and have a good time. Jeannie refused to marry and in return, gets a two thousand year nap and a handsome, loving (if not uptight) master who instantly frees her and doesn't demand anything from her. Jeannie's sister got two thousand years of involuntary servitude under a series of cruel, stupid and neglectful masters. She takes full advantage of having magical powers but that doesn't mean she asked for them.
Celebrity Paradox applies to both I Dream of Jeannie and BewitchedEach is a television show in the other show's universe.