The key phrase here is; "In establishing the validity of the tag, the fielder shall hold the ball long enough to prove that he has complete control of the ball. If the fielder has made a tag and drops the ball while in the act of making a throw following the tag, the tag shall be adjudged to have been made." Another way of putting it is that the release of the ball after a tag must be "voluntary and intentional."
In a DP situation, the benefit of the doubt is often given to the fielder making the turn because the transfer of the ball from the glove to the throwing hand happens quickly. In the OP description of the play the release of the ball did not appear to be voluntary and intentional. So, as long as the runner did not intentionally interfere, I do not have an out on that play.