I've never seen anything like this.
At the 0:19 mark, the home plate umpire signaled 'time', thus blocking the runner at second from legally advancing to third. The runner did so anyway. Nashville then put the ball in play with the runner advanced without appeal. At that point, the runner should have been awarded third base since Nashville declined to object.
In the end, it looks like the umpire sent the runner back to second and replayed the at-bat, which in my opinion was dead wrong. The at-bat should have stood (fly out to LF), and the runner should have remained at third base.
The proper action for Nashville should have been for the pitcher to step off the rubber, toss the ball to the 3rd baseman, and tag the runner out for being off second base. At that point, the runner would either be out, or the umpire would have sent him back to second.