ST. PETERSBURG, Fla. — Carlos Rodon made his first minor-league rehab start Tuesday for Winston-Salem, and while the White Sox lefty overpowered Class A hitters with 6 strikeouts in his first 2 innings, he also gave up 5 runs on 4 hits, including a home run.

Rodon faced 16 batters and threw 71 pitches, 43 for strikes, over 3? innings. He walked two.

It was Rodon’s first game action since his only start of spring training on March 19, when he struck out five and gave up 1 hit in 4 innings of scoreless ball against the Los Angeles Angels.

Rodon was placed on the disabled list with upper-biceps bursitis the day before Opening Day.

Initial reports from Zebulon, North Carolina, where Rodon faced the Carolina Mudcats, had Rodon touching 96 mph, according to the speed gun at Five County Stadium. In the first inning, Rodon struck out the first two batters on three pitches and the third batter on four.

Second baseman Luis Aviles hit a 2-run homer in a 3-run second inning for the Mudcats. Rodon also struck out the side in the second.

Jones, Putnam still not close:

Right-handers Nate Jones and Zach Putnam, both dealing with elbow issues, and infielder Tyler Saladino (back) are not with the Sox on the road trip.

Jones, on the disabled list since May 4 with elbow neuritis, was throwing bullpens before the trip but has not since last week, which raises questions about his progress. But manager Rick Renteria wouldn’t characterize Jones not throwing sidelines as a setback.

“They’re still recovering and getting treatments,” Renteria said. “They weren’t picking up the ball when we first left.

“It’s not a setback (for Jones). He was being treated with, as far as we’re concerned, with just a lot of our patience. Being very careful. We want to make sure these guys come back ready to go. More precautionary than anything else.”

Garcia moves up in votes:

Avisail Garcia moved up one place in All-Star Game voting for American League outfielders. Teammate Jose Abreu, an all-star in 2014, would like to see his teammate play in the July 11 event at Miami but would caution Garcia.

“I always want the best for him, but my advice is to keep doing what he’s doing, don’t pay attention to the All-Star Game and keep your mind on what you’re doing,” Abreu said through translator Billy Russo. “His numbers will be there for the fans to vote for him. Just concentrate on what you’re doing.”

Going into Tuesday’s games, Garcia ranked among AL leaders in average (fourth, .330), multihit games (fifth, 20), RBI (seventh, 39) and slugging (10th, .532).

“We’re not surprised by his breakout season,” Abreu said. “He has the talent. The difference this year is his mindset and focus. We’re enjoying being around it because we knew this is the kind of player he could be.

“His numbers will be there. If he’s in the All-Star Game, that will be good. But the most important thing is he’s helping the team.”

This and that:

• Right-hander Michael Kopech and left-hander Jordan Guerrero from the White Sox’s Class AA Birmingham club were named to the North Division roster for Southern League All-Star Game on June 20 in Pensacola, Florida.

*The Sox signed 32-year-old veteran Bobby Parnell to a minor-league deal.

• This report was produced in partnership with the Chicago Sun-Times. For more coverage, check chicago.suntimes.com.