Anderson, named the organization's Pitcher of the Month for April, had not allowed a run in 20 consecutive innings covering his last three starts prior to being called up to the Majors for the first time.
The right-hander was 4-2 with a 0.69 ERA in 39 innings with Mobile. Gibson said that right-hander Trevor Cahill, who was moved to the bullpen in mid-April after four starts, would remain a reliever.
Cahill, 8-10 with a 3.99 ERA last season in 26 games, including 25 starts, is 1-5 this season with a 6.59 ERA, but he has not allowed a run in five of his last six appearances.
"We're going to leave him in the bullpen right now, that's what we talked about," Gibson said. "He had one hiccup. He's throwing the ball better and then get got sick. Then he threw OK in his first game here. We'd like to see him repeat that, be consistent with it. That's what we need. I haven't really talked to him in a while about it, but I think he's kind of enjoyed the switch. It's different for him and he's responded well to it."