Zuko would've come during the inspections. I imagine he'd have been stationed at a seedy prison hold somewhere on Whale Tail Island, near the base of the Southern Raiders. They police the Southern Water Tribe and hand out rations from Earth Kingdom colonies nearby.
Aang would've outwitted him during a visit, unveiling that he was the last airbender. I think it might've sent Zuko into overdrive.
Aang's playfulness and bravery inspires the entire village to revolt against the occupation, and it's this that prompts Katara and Sokka to escort the young Avatar on his journey to the North.