Domi, who was selected No. 12 by the Coyotes in the 2013 NHL Draft, had 135 points (36 goals, 99 assists) in 222 games over three seasons with Arizona.
"You didn't get recognized much there," he said.
The same can't be said for life in Montreal, where the sport is part of the cultural fabric of the community. Domi is comfortable in such a hockey fishbowl, having grown up in it while his father, Tie, was playing for the Toronto Maple Leafs from 1995-2006.
With players such as Mats Sundin and Curtis Joseph around, it was the type of environment that prepared Max at a young age for the constant attention that comes with playing in Montreal. In the process he also learned that the best players in the game put in countless hours of sweat to be just that.
"Yeah, I think obviously on the ice is one thing, but then off the ice, seeing how hard those guys worked in all that stuff, it translates to how I came into the NHL myself, taking those habits and trying to put them into my daily routine," Domi said. "When you're 5, 6 years old and you see guys like Mats Sundin after a game, sweating on a bike after an overtime win, that sticks with you your whole life and those are the lessons I've learned."
It also helped him deal with the spotlight.
"The tradition of hockey as part of life in Montreal is so deep rooted and Max has embraced it from Day One," said Tie, 49. "He knew what he was walking into. He knows the NHL life. It's kind of what he grew up in in Toronto. And now he's living his dream. Not to take away anything away from Arizona. He played three years there. He really enjoyed himself there. But then he was traded to Montreal. And now it seems he's really embraced the pressure.
"I think he's adapted so quickly because he was around so many great players and role models since he was a kid. Mats, Mario (Lemieux), Teemu (Selanne), those guys are my close friends. They're his uncles. He's been around them his entire life. And he saw how humble they were no matter how much success they had. Especially Mats and Mario, they've prepared him for the next stage. He takes what they say to heart far more than he does me, especially when it comes to scoring goals. He's matured a lot. He jokes now, he says he wishes he would have listened to me earlier."
Joseph, the Maple Leafs' starting goalie from 1998-2002, said it wasn't from a lack of trying on Tie's part.
"I remember all you would hear from the boards was Tie yelling, 'Max, Max Max,' when Max was out on the ice playing as a boy," Joseph said with a laugh.
On game nights in Toronto, young Max would spend hours playing ministick hockey with two of Joseph's sons, Taylor and Tristan, in the team family room. Taylor was a year older than Max, Tristan a year younger.
"They'd gang up and try to intimidate Max," Joseph said. "But it's hard to intimidate a Domi.
"The man Max has grown into is amazing and inspirational. Coming into Montreal, he could have handled it two ways. He could have arrived with a sense of entitlement, being the son of a well-known ex-NHLer. But it says a lot that he's done it with humility and respect."