After a year on loan at Crystal Palace, Gallagher is now back at his boyhood club trying to break into Tuchel's first-team plans ahead of 2022-23.
While there is every expectation that the England international will challenge for a spot in the starting lineup this season, Tuchel has been consistent with his stance that the returning players must make an impression.
Gallagher played the opening 45 minutes in Las Vegas, the game remaining goalless at the break and the 22-year-old picking up a yellow card.
Nevertheless, Gallagher's performance was one of the plus points as Chelsea eventually recorded a 2-1 victory over their Mexican opponents courtesy of goals from Timo Werner and Mason Mount.
Speaking to reporters after the game, Tuchel said: "With Conor, the same as a midfield player. Conor trains at a really high level, and you can clearly see it was the right decision to let him go on loan. He made a huge step in his development at Crystal Palace and became an England player. We can see this clearly in training. It was a very good start and a good match for him.
"Now, for him, it's important he gets used to our principles of the game, to understand when to move and when not to move, and his work rate is outstanding, and he has such a big heart. He can be a big asset for us."
Tuchel shared a similar opinion when quizzed on Ethan Ampadu, who is back with the West Londoners after a season out in Serie A with Venezia.
Although his Italian side were relegated to the second tier, the Wales international benefitted from 26 starts and three substitute appearances in the league.
Having played in a three-man backline and midfield during his time in Italy, the 21-year-old was used in the centre of Tuchel's three-man defence during the second half.
When quizzed on whether Ampadu had a chance of remaining at Stamford Bridge for the upcoming campaign, Tuchel spoke positively about the versatile youngster.
Tuchel added: "Everybody has a chance. Ethan did very well, I think. The position is a good position for him in the middle of the back three.
"He played a lot of vertical passes and did not play left to right only. He played through the lines with his passes and dribbles. So he was very active, and it was a good match for him. He is training well."
Chelsea are next in action when they take on MLS side Charlotte FC on Wednesday evening.