As far as recent second generation stars go, it's mostly because the majority of their dads worked for the WWE, have friends in the WWE, and can insure a push in the WWE. The Harts have never had any real presence in TNA (Teddy Hart might have been there briefly, I'm not positive), and while Dusty Rhodes worked there, he's got much better connections in the WWE. To my knowledge the DiBiases have never set foot there. The Colons could have opted to go there, but considering they both needed a good developmental system to work through, the WWE was the logical place. Jesse...well, Jesse really wouldn't have made a difference.
Jeff Jarrett and BG James only marginally count, considering JJ founded the company and BG is his bromance. So really, TNA just isn't a hot attraction for second gen stars, most of whom get their start by their dads making connections for them. In time, some might jump ship, but really, there's nothing attractive for them there when they can get a much easier ride into the WWE.