If Control of a Battlefield is Contested, there aren’t units controlled by different players there, and the turn is in a Neutral Open State, a Showdown is opened during the next Cleanup. See rule 318. Cleanups for more information.
§ 344.2 Core Rules PDF (officieel)
§ 344 A Showdown begins when Control of a Battlefield is Contested during a Cleanup and the turn is in a Neutral Open State.
