But neither seemed bothered by the move, which took away a possible job opening, as they went through their drills at the Canadiens rookie camp on Friday.
"We play similar styles," said the six-foot-six Tinordi, who like Murray is a stay at home blue-liner who likes to hit. "I think I can learn a lot from him in the main camp.
"He's a good player and I think he'll help this team a lot with his physical play. But as far as looking at it as my spot, I don't think so. I'm just going to play my game and see what happens."
Tinordi spent most of last season with Hamilton in the AHL, but was called up for eight regular season games and stayed on for the post-season as the Canadiens were eliminated in five games by the Ottawa Senators.
He looked like a strong candidate to start the 2013-14 campaign in Montreal, but now the top-6 on defence looks to be booked by P.K. Subban, Josh Gorges, Andrei Markov, Rafael Diaz, Francis Bouillon and Murray, with the re-signed Davis Drewiske as the seventh man.
Murray was signed mainly to fill in for Alexei Emelin, who blew out a knee late last season and will be out of action until at least December after reconstructive surgery.
Still, a youngster like Tinordi or Beaulieu can still play his way into the mix with a strong camp. That's what both hope to accomplish.
"I've just got to play hard, be physical and play with an edge," said the son of former NHL defenceman Mark Tinordi. "I think my puck skills have improved too, so I want to show that, and my skating.
"I have high goals for myself. I want to play in the NHL this year, but as far as looking at it as a disappointment (if he doesn't), I wouldn't say that."
Beaulieu, 20, is a offensive defenceman and power play point man, who would be more likely to move in if Markov, Subban or Diaz is injured. He played six NHL games last season, picking up two assists.
"Look at the guys they signed — I don't feel they fit my type of game," said Beaulieu. "But I'm here trying to make the team. I'm not looking at the numbers.
"If I'm ready to play, hopefully I'll get an opportunity. Management has been spectacular with me so far, so I have no doubts about that."
Beaulieu, the Canadiens first round pick in 2011, spent the summer living near the Canadiens training facility and working out daily with conditioning coach Pierre Allard.
His got himself into trouble in April when he and his father, former Sarnia Sting coach Jacques Beaulieu, were charged with assault after getting into a fight at a charity golf tournament.
However, after pleading guilty, Beaulieu was given a conditional discharge, so he will not have a conviction on his record.
"It's over with," he said. "It's been handled and it's all about the future now.
"I've already forgotten about it. The organization's forgotten about it. So, it's over and done with. I'm relieved, and it's time to play hockey."
At camp, he wants to show the Canadiens that he has taken a step forward as a person and a player.
"I've been trying to take on more of a leadership role," he said. "It's my third (camp), so it's important to make an impression early and show that I've matured, grown up."
Other defencemen with NHL aspirations for this season include Greg Pateryn, who looked good in a three-game call-up by the Canadiens last season, and 2011 draft pick Magnus Nygren of Sweden. Morgan Ellis, who spent a first pro season in Hamilton in 2012-13, and Saskatoon Blades Darren Dietz and Dalton Thrower are also in camp.
Among the forwards are hulking first-rounder Michael McCarron, who will spend this season with the OHL's London Knights, Kamloops Blazers scoring star Tim Bozon, and former Shawingan Cataractes captain Michael Bornival, who has an outside shot at making the jump to the NHL.
Also in camp is Justin Courtnall, the 24-year-old son of former NHLer Geoff Courtnall and nephew of ex-Canadiens winger Russ Courtnall. He signed an AHL contract to play in Hamilton, but hopes to crack the NHL lineup.
"My uncle Russ was extremely happy and my dad as well," said Courtnall. "My uncle has only great things to say about the city.
"He was a great player and lots of fun to watch. Very fast. I hope I can come close to his reputation here."
Asked if he played like his uncle, Courtnall said: "Maybe the skating, but a bit more physical. More like my dad, I'd say."
Another player to watch in camp is goaltender Zach Fucale of the Memorial Cup champion Halifax Mooseheads. He was drafted 36th overall in June. With Carey Price and Peter Budaj set in goal, Fucale is almost certain to return to the Mooseheads, but hopes at least to make it to the main camp, which opens next week.