Olivo, who had seen little playing time recently as the Marlins' No. 3 catcher, departed Friday after batting practice and before the team's game against the St. Louis Cardinals.
"I've never been involved in something like that -- to have somebody just leave after batting practice," Redmond said. "I think everyone was kind of in shock. I know it wasn't an ideal situation for him, not getting to play a lot, but at the same time the team relies on you."
Olivo had a .203 average in 33 games this year with the Marlins. He became the No. 3 catcher when Jeff Mathis was activated from the disabled list May 14 and had only 15 at-bats since then.
Outfielder Jordan Brown was recalled from Triple-A New Orleans on Saturday to take Olivo's roster spot.