He was tied for the lead in hits with Angels rookie Mike Trout, and is second only to Trout in stolen bases with 11 in 13 tries in June.
Revere, who led the team with 34 stolen bases as a rookie last season, has 15 on the year to rank tied for fourth in the American League despite playing in just 41 games entering Wednesday.
"He's pretty good at anticipating," Twins manager Ron Gardenhire said. "But it's a learning process. There's times where he'll take off and you say he has no chance, but he outruns the ball sometimes, which is nice to have that kind of makeup speed where you can outrun that mistake."
Part of that learning experience comes with knowing when to run, as it's obviously easier to steal on a breaking pitch than a fastball.
"He's getting better at reading breaking-ball counts," Gardenhire said. "Reading when a guy is throwing curveballs or balls in the dirt. So he's getting better at it. It's a work in progress."