The 27-year-old Tomlin is expected to be activated from the 15-day DL in time to make his sixth start and seventh appearance of the season.
The Indians right-hander has been sidelined just over two weeks with right wrist soreness and was placed on the DL May 12 (retroactive to May 8) after being diagnosed with intersection syndrome, a condition that caused inflammation of a tendon and tendon-sheath in his right throwing wrist.
"Josh threw a good bullpen," Indians manager Manny Acta said after the pitcher threw on Tuesday. "I was there to witness it. He threw the ball well and he threw all his pitches."
Tomlin will be making his first start since taking a no-decision in Game 2 of a doubleheader against the White Sox on May 7.
He pitched 7 1/3 innings, allowing five hits and two earned runs while striking out eight and throwing 104 pitches in that game, a 3-2 Indians victory.
Tomlin is 1-2 with a 4.67 ERA this season and is seeking his first victory at home.
Adcock, a 24-year-old right-hander, was recalled from Triple-A Omaha for the third time on May 19 to start against Arizona at home the next day.
He held the Diamondbacks scoreless through the fourth inning, then allowed a run in his fifth and final inning.
Adcock began the season at Omaha where he produced a 3-1 mark and a 1.37 ERA in 26 1/3 innings (four earned runs). He was first recalled by the Royals on April 28 and has been optioned to the Storm Chasers twice since then, though he has not pitched for Omaha since April 22.
The Royals like Adcock's potential and decided to bring him back for another start despite the loss to the Diamondbacks.
"We're kind of looking at some different scenarios and some different things," Royals manager Ned Yost said then.
Royals: Bullpen doing the job
The Royals received superb relief pitching in winning consecutive games against the Orioles Saturday and Sunday, giving up just four singles in 7 2/3 innings.
Jeff Francoeur was 7-for-12 in the three-game series against the Orioles. In his last 14 games, the right fielder is batting .379 with all five of his home runs this season, two of them on the trip to Baltimore.
Indians: Cabrera to test hamstring
Indians shortstop Asdrubal Cabrera, who is dealing with a tight left hamstring, will run and take batting practice on Monday. He hasn't played since leaving Friday night's game against the White Sox in the seventh inning.
Royals center fielder Jarrod Dyson sat out Sunday's game a day after a frightening collision with left fielder Alex Gordon. Dyson sustained a bruised hamstring, but said he was fine.