The crew didn't know much about Prince Zuko. The royalty and nobles as good as lived in another world from the common people; everyone knew the crown prince's name, but beyond that was mostly speculation for all but the highest tiers of society.
The crew of the Wani was not exactly resplendent with nobility. Pieced together from demoted officers and unlucky navy men, they were a ragtag group. The best that a banished prince could hope for. Or rather, the best that the crew members themselves thought a banished prince could hope for—no one knew what the prince in question thought about the situation. And the crew certainly knew enough about royalty in general to know not to ask.
So no one was sure what to expect when they set sail for the first time. The prince was presumably on board, though no one saw him for a few weeks. The esteemed General Iroh was similarly rarely seen at first, spending most of his time in the prince's quarters or speaking with the ship's doctor.
The crew then made an amateur mistake: they began to relax. Maybe this gig won't be so bad, they thought. Maybe we'll just sail around and bow when the royals walk by and otherwise get to stay out of trouble. Then the prince emerged and dashed their hopes.
When Prince Zuko suddenly made his first appearance on deck, the sight of him startled the blazes out of nearby crewmen. They stared at him, frozen, for several seconds before remembering themselves and saluting clumsily. The young prince's face was still half-bandaged, and the visible side was clenched tightly in pain. General Iroh hovered just behind him, clearly worried.
"There is no hurry," the general was saying. "You should rest more before worrying about our route."
"There is no time to waste, Uncle!" The prince snapped in return. "I have wasted far too much already. We need to set a deliberate course if we're going to find him. Where are we now?" He spotted Lieutenant Jee, the ship's highest commanding officer, standing by the rail at the stern.
"Show me," were Prince Zuko's first words to Jee. Quite rudely spoken, too.
"Sir?" Jee said. Not the best first words back, admittedly, though at least he'd managed a proper salute.
"Show me where we are right now! On a map!" The prince appeared frustrated that Jee hadn't immediately understood his meaning.
"Of course, sir. Right this way," Jee said stiffly, leading the way to the navigation room.
Their relationship did not improve after the first meeting. Nor did the prince make a good impression with anyone else on the Wani.
He was, quite frankly, a brat. He was every inch the barely-teenage boy: loud, disrespectful, headstrong. He ordered the crew around like they weren't really people, expecting them to work tirelessly and without complaint for as long as he wanted. He offered no gratitude for their hard work, nor explanations for their ridiculous quest.
It got old quickly.
Not the most patient or undyingly loyal to begin with, the crew fast grew displeased with the prince's behavior. It rankled to be under the thumb of a boy not even old enough to grow peach fuzz on his face.
But General Iroh's presence and efforts went a long way to smooth things over. He handed out apologies on behalf of the prince, softened his nephew's words, and (in the worst cases) stood as an authority figure that none dared cross.
Eventually, the ship reached an equilibrium. The crew members settled into working with new crewmates, and the royalty seemed to settle into life on a ship. Prince Zuko's open wound began to scar over, presumably reducing the pain somewhat. Not that anyone said anything to him about it. The ship's doctor was the only one besides General Iroh who would discuss it with the prince, and sadly the medic wasn't much of a gossip.
The ship was still in the dark on why they were escorting Prince Zuko around the globe—let alone why they were hunting the legendary, long-gone Avatar—but the sailors didn't care that much for the details, anyway. It was no great glory to them, just a living.
Thus more or less content (or perhaps just resigned) to sail around according to the prince's shouted directions, the ship's crew was not prepared for the shift in the prince's behavior a few weeks later.