I see that when I start the dip the shoulders lower quicker than the barbell. This is what I would expect even if there were no hands that pushed against it. That is because the body shortens which makes the shoulders descend quicker than gravity alone can explain. The barbell however will only descend as quickly as gravity makes it, unless the lifters pulls it down.
You may be right though that I unconsciously push against the bar when I initiate the eccentric part of the lift and thereby increase an effect that would otherwise be totally negligible. I will try what happens when I actively focus on NOT driving up before the bounce has happened.