If I conquered a battlefield on my turn, then my unit leaves and returns to that battlefield during my opponent's turn, does this count as a new conquest instance?

Ruling: Yes, this counts as a new conquest instance and you score a point.

Sequence:

• When your last unit leaves an uncontested battlefield, you lose control of that battlefield
• When your unit returns to the now-open battlefield during your opponent's turn, you conquer it again
• You score a point because you did not already score on that battlefield this turn (it's your opponent's turn)

Nuances:

• The key factors are: (1) you did not score on that battlefield this turn, and (2) you lost control when your last unit left the uncontested battlefield