Rivers had told the San Diego Union-Tribune that it was a "relief" to start camp without Tomlinson looming over the team.
"I don't know how everyone feels or if they felt it," Rivers told the newspaper. "Maybe it was a little bit of a relief. Maybe it's a feeling of, 'I can do a little more without wondering what he thinks.'"
The 31-year-old Tomlinson signed with the Jets this offseason after being released by the Chargers. He had his worst season as a Charger in 2009, rushing for just 730 yards, although he did score 12 touchdowns. It was his first season with fewer than 1,000 rushing yards in San Diego.
"The thing, honestly, about Tomlinson is if he's coming down, he's coming down from the very top of the mountain," coach Rex Ryan said. "It's not like he was three-quarters of the way coming down."
Tomlinson spent eight seasons in San Diego, rushing for 12,490 yards and 138 rushing touchdowns. He also caught 530 passes for 3,955 yards and 15 touchdowns, and was named the NFL's MVP in 2006.
Tomlinson, the unquestioned starter in San Diego, will compete for carries with Shonn Greene on the Jets.
"This is my first time going live in practice in all my years and I love that because it's football, and you're going to get hit," Tomlinson said. "The quicker you get acclimated to getting hit and being on the ground, it's better for you when the games start."
Tomlinson routinely would see limited action in the preseason with San Diego, not playing much -- if at all -- during games. He'd like that to change this summer.
"I want to play," he said. "I want to be with the guys. Everybody else is going to play and I want to be a part of that."
The five-time Pro Bowler told the Post that he's focused on his current team, not his former home.
"Honestly, I really have no reaction to it," he told the Post. "I don't spend any of my time thinking about what's going on there because I'm so focused in this football team and job at hand. I've moved on."
Gates had told the Union-Tribune that Tomlinson had a star status, something that Rivers doesn't demand.
"He has done a phenomenal job with opening relationships with people," Gates told the newspaper. "When you talk about great player, you have to be careful what you say. Obviously, I miss LT. I played with him a whole lot. But the reality is Philip and I have a more core friendship because of the openness.
"Me and LT had a wonderful relationship too. But sometimes you got the sense of stardom status and you can only take it so far. With Philip, I never feel that."
Tomlinson insists he has always been a good teammate, despite what some Chargers players might say.
"We all had a great relationship and I never put myself in position to be bigger than the team," Tomlinson said. "I mean, I never act like that. So, it was surprising, but, it is what it is and guys are going to feel differently and I'm moving on."
Tomlinson told the Post that he's not surprised with the comments as he watched Junior Seau go through the same thing when Seau left San Diego.
"It doesn't hurt me, but nothing surprises me because guys want to speak their opinion on things. Junior Seau went through the same thing with guys when he was the big star and he left the team and guys said how they felt about him. It's the same situation. Good luck to those guys," Tomlinson told the Post.
Information from The Associated Press contributed to this report.