Maybe a nerve twitch but.. the jaw goes slack/limp when you die. So I think the pressure of him pushing the head down is simply moving the jaw forward.
look at it agian, he never pushed down on it, the thing almost jumped out of his hand...
yep.. kudos to whoever posted the video of Joe explaining what happens in guillotine executions... even more bizarre is one vomiting after being beheaded which has been caught on video as well (rare)