Safe on both.
Voluntary release has nothing to do with this though - you guys are mixing your rules.
Picture this... Runner comes in sliding, fielder applies tag and has possession of the ball. Then A) as she's switching hands for a double play or B) runner pops up from slide and hits the glove (separate contact from the tag), and the ball comes out. In both A and B, you have a valid tag (and no voluntary release), and you have an out.
In the OP, it is obvious from the description that the ball was not held securely at the moment of the tag, since the tag itself caused the ball to dislodge. The fielder's ability to regain possession has nothing to do with it. Safe.