Does a Showdown still occur at a scored battlefield when a player moves a unit there after moving all their units out?

Ruling: Yes, a Showdown always happens if a unit applies contested to a battlefield.

Sequence:

• Player holds battlefield and scores a point
• Player moves all units out (no one controls it)
• Player moves another unit in
• Showdown occurs (though no point is scored again)

Nuances:

• A Showdown is triggered whenever a unit moves to a battlefield they don't currently control, regardless of whether the battlefield has already been scored