On September 2, 2003, while with the Cubs, Alfonseca was thrown out of a game for bumping an umpire with his stomach. He was subsequently suspended for five games.
After the 2004 season, he filed for free agency, and signed back with the Marlins, but in July 2005, he suffered a right elbow injury and missed the rest of the season. He was released by the Marlins, signed with the Rangers, but after another mid-season elbow injury was released by them. The Phillies signed him in January 2007.
His nicknames are El Pulpo ("The Octopus"), The Dragonslayer, and Six-Fingers. He has six fingers on each hand and six toes on each foot, a condition known as polydactyly. His grandfather also had this trait. Alfonseca regards it with pride, as a kind of family emblem.
Alfonseca and his wife Rocio have two sons: Antonio, Jr. and Mark Anthony, and two daughters, Jenitza and Asia .