Explanation by bobdahaxor:
This is actually a demonstration of damped harmonic oscillation. The metronome needles are at the same speed and the only variable left is time. When he adds the board there is a transfer of angular momentum because of the phenomenon of angular momentum as a generator of rotation. As the soda cans move, angular momentum is being transferred from the needle, to the system and cans. This transfer of angular momentum is the damping force. This and conservation of angular momentum makes the needles sync.