If someone moves back from a battlefield they occupied and then moves in with a new unit so it's no longer empty, does it count as a conquer again in the same turn?

No, that does not count as a conquer again in the same turn.

According to Rule 447, a player may only score from a battlefield once per turn. Furthermore, as established in the FAQ:

• Ruling: You cannot conquer a battlefield that you already scored from (via holding or a previous conquest) during the same turn.
• Nuance: Moving a different unit into a battlefield you already control does not allow you to conquer it again. Conquer only occurs when a player gains control of a battlefield they did not yet score this turn.

Even if you move your units out and move a new unit back in, the battlefield remains one that you have already scored for the turn, so no additional points or "when you conquer" triggers will occur.