The Scotland captain is set to return to action when the Warriors welcome Ulster to Scotstoun in the United Rugby Championship on Saturday.
Tuipulotu was rested for last weekend's 26-20 victory over Munster at Thomond Park following a demanding 2025/26 campaign and summer, which included international duty with Scotland and the British & Irish Lions.
Smith believes the 29-year-old has benefited from a proper break ahead of his return.
"He's had a proper break of six weeks. I think he's had a decent recovery like everybody else," said Smith.
"I also think there's a lot of expectation around everything this year. And I want him to manage that through concentrating on the way he plays, what he wants to improve on and how are we going to make him the best version of himself. He's on a journey still.
"He knows that. So no extra pressure on him. I hope he doesn't feel this expectation.
"I hope nobody feels expectation in this environment because I think we've got to earn that right again."
Tuipulotu's return comes as Glasgow prepare for their first competitive match at Scotstoun this season, with Smith keen for his squad to focus on the challenge immediately in front of them rather than what has gone before.
"We start over. We finished on a disappointing note last season. We need to rebuild and refocus," he said.
"Not rebuild the team, but rebuild the season from the first day here at Scotstoun."