Anderson, who led the Blue Jackets with 214 hits during the regular season, leads them in the postseason with 21, five more than linemate Nick Foligno.
"He's been a difference-maker every time he's on the ice," Foligno said. "For him, that's going to be the biggest challenge and will continue to be his whole career, and it's not easy to do. The guys who are elite in this league are consistently doing it every night. He's got a hard task because he's a big power forward who needs to play physical, and it's hard on your body."
Anderson set NHL career highs this season in goals (27), assists (20) and points (47), and his plus-25 in 82 games was the best on the Blue Jackets and tied for sixth among NHL forwards.
He admitted that he sometimes got away from the physicality Tortorella wants to see from him.
"It's hard to play that style for 82 games," Anderson said. "When you're having so much success at the beginning of the year, goals going in and points going your way, it's easy to get away from that.
"When important games come down the second half of the year, you have to get back to the way he wants you to play. He harped on me about that. It's good when you have a coach like that who's always on you. It just makes you a better player."
Anderson had eight shots on goal and was minus-1 against the Lightning, numbers that are irrelevant to Tortorella.
"Some of the early hits on (Lightning defenseman Victor) Hedman and players like that were crucial in that series," Tortorella said. "His mind has been in a good spot. He's so important to this club in playoff hockey."
The Blue Jackets, who haven't played since Tuesday, practiced Friday and Saturday. They were off Sunday and will hold a scrimmage at Nationwide Arena on Monday.