If I've already scored a battlefield this turn, does the order of moving units out and in matter for triggering a showdown?

Ruling: Yes, the order matters. If you move a unit out first and then move another unit in, you lose control temporarily and trigger a showdown when the new unit arrives. If you move the new unit in first before moving the original unit out, you maintain control throughout and no showdown occurs.

Sequence:

• Moving unit B in first, then unit A out: You maintain control at all times, no showdown
• Moving unit A out first, then unit B in: You lose control when A leaves, battlefield becomes contested when B arrives, showdown begins

Nuances:

• Opponents cannot react to unit movement itself, but can interrupt during a showdown if one is triggered
• Units with movement triggers (like merchant) can still be responded to