Tallet, 34, was with the Pirates' Triple-A affiliate before signing with the Padres. He's a nine-year Major League veteran having pitched for three teams (Blue Jays, Indians and Cardinals).
Tallet's best season came with the Blue Jays in 2008 when he had a 2.88 ERA in 51 appearances. He split last season between the Blue Jays and Cardinals.
Tallet pitched two innings in relief for Tucson on Saturday against Fresno. He allowed one run on two hits with four strikeouts.
Tucson needed a pitcher after reliever Brad Brach was added to the Padres' Opening Day roster on April 5 after Tim Stauffer went on the disabled list with a strained right elbow.