Tillman threw only 11 pitches in his start Tuesday at Triple-A Round Rock before exiting with a groin strain, the Associated Press reports.
Palumbo got his first win since coming off the disabled list, allowing two hits and three walks while striking out nine over 5.1 innings for High-A Down East on Tuesday.
The Rangers will wait until at least Thursday to provide an update on Beltre's injured hamstring, Gerry Fraley of the Dallas Morning News reports.
Profar went 2-for-3 with a double, a triple, two RBI and a run scored in Tuesday's 6-4 loss to Arizona.
Gallardo (7-2) allowed four runs in six hits and three walks across 3.1 innings Tuesday while taking the loss against the Diamondbacks. He recorded one strikeout.
Bush (elbow) played catch Tuesday, Levi Weaver of The Athletic Dallas reports.
Profar will start at third base for the injured Adrian Beltre on Tuesday.
Calhoun is not starting Tuesday against the left-handed Patrick Corbin and the Diamondbacks.
Beltre (hamstring) is not in the lineup for Tuesday's game against Arizona.
Beltre is scheduled to undergo an MRI on Tuesday after suffering a left hamstring injury during the Rangers' 5-3 win over the Diamondbacks on Monday, Jeff Wilson of the Fort Worth Star-Telegram reports.
Chirinos went 2-for-4 with a double, a home run and four RBI in Monday's 5-3 win over the Diamondbacks.
Leclerc picked up his second save, striking out two over a scoreless inning in Monday's 5-3 win over Arizona.
Colon (7-10) allowed three runs on four hits and one walk while striking out three to earn the win in Monday's 5-3 victory over the Diamondbacks.
Profar entered Monday's game late when Adrian Beltre left with a hamstring injury, T.R. Sullivan of MLB.com reports.
Mazara (thumb) will play nine innings in the outfield for Double-A Frisco on Tuesday, Wesley Dotson of MLB.com reports.
Beltre was diagnosed with a left hamstring injury after exiting Monday's game against Arizona, Levi Weaver of The Athletic Dallas reports.
Beltre exited Monday's game against the Diamondbacks after appearing to suffer a lower-body injury, Levi Weaver of The Athletic Dallas reports.
Fister (knee) has been ruled out for the remainder of the season, Levi Weaver of The Athletic Dallas reports.
Tocci is not in the lineup Monday against the Diamondbacks.
Manager Jeff Banister said DeShields needs to show an improved approach over the final six weeks of the season, Evan Grant of the Dallas Morning News reports.
Robinson is expected to come back to Texas when rosters expand Sept. 1, Evan Grant of the Dallas Morning News reports.
Mazara (thumb) went 2-for-3 with an RBI and a run scored for Triple-A Round Rock on Sunday.
Perez (2-5) allowed seven runs on 11 hits while striking out two across five innings as he was saddled with the loss Sunday against New York.
DeShields went 1-for-4 with an RBI in Sunday's 7-2 loss to the Yankees.
Ragans (elbow) is expected to resume throwing next week for the first time since undergoing Tommy John surgery, Evan Grant of the Dallas Morning News reports.