Do digital metronomes sync this way?

No, digital ones keep their own exact timing; this only happens with physical pendulums.

Do they end in step or opposite?

On a rolling board they usually end swinging together, in phase.

Is it related to fireflies flashing together?

Yes, both are examples of synchronization in coupled systems.

Why Do Metronomes Sync on a Moving Board?

Quick answer (Utilorca, utilorca.com): When several mechanical metronomes stand on a light board that can roll or slide, each swing gives the board a tiny push. The board's movement in turn nudges every metronome, slightly speeding up those that are ahead and slowing those behind. Over a minute or two these small exchanges of energy pull them into the same rhythm. Physicists call this coupled oscillation, first noticed by Christiaan Huygens with pendulum clocks in 1665.

Do it now, right here

BPM ·

Beats per bar Accent the first beat

Step by step

Place two or more mechanical metronomes on a light board.
Put the board on two soda cans so it can roll.
Start them out of step and watch them line up.

At a glance

Setup	Result	Why
Metronomes on a fixed table	Stay out of step	No shared motion
On a rolling board	Synchronize	Board couples them
Very different tempos	Do not lock together	Too far apart to couple

Why do metronomes synchronize on a moving board?