When you charm an opponent's unit into an empty battlefield on your turn, does the opponent score a point? If you then move your own unit there and win the showdown, do both players score a point on the same turn?

Ruling: Yes to both. When you charm an opponent's unit into an empty battlefield on your turn, they score a point. If you then move your own unit there and win the showdown (their unit dies, yours survives), both players score a point on the same turn.

Nuances:

• You cannot win by conquering alone, so if your opponent had 7 points and you gave them the 8th point through conquering on your turn, they wouldn't win unless you also gave them a conquering at another battlefield that same turn.
• If you reverse the order (move your unit to empty battlefield first, then charm opponent's unit there), the charmed unit becomes the attacker and your unit is the defender, because control of the battlefield determines attacker/defender status, not whose turn it is.