Alosi was a linebacker at Hofstra University from 1996 to 2000. As a senior, he was named the co-recipient of the Mayor’s Trophy, an annual award presented to the two Hofstra players who best exemplify good sportsmanship and fair play both on and off the field. He won the award in 2000, despite having been arrested the year before for allegedly breaking into a dorm room with seven teammates and assaulting three students. Originally charged with third-degree assault, he later pleaded guilty to a lesser charge of second-degree harassment, a misdemeanor.
He became a coach for Hofstra in 2001, then moved on to the New York Jets in 2002. In 2006, he joined the coaching staff of the Atlanta Falcons. He was hired as the Jets' strength and conditioning coach in 2007.
During a game against the Miami Dolphins on December 12, 2010, Alosi stuck out his knee and tripped Miami gunner Nolan Carroll, who was running down the sideline during a punt return. Two days later, the Jets suspended him indefinitely after it was discovered that he had instructed inactive Jets players to line up along the sideline so as to potentially impede opposing players. General manager Mike Tannenbaum said that Alosi had initially not been truthful about how the wall had been formed. Alosi was fined $25,000 by the Jets and suspended for the remainder of the 2010 season. The NFL subsequently fined the Jets $100,000 for Alosi's actions.
Alosi resigned from the Jets on January 31, 2011, and has not worked in the NFL since the tripping incident.
Alosi worked as the head strength and conditioning coach at Bryant University in Smithfield, Rhode Island for the 2011-2012 season. He worked primarily with the lacrosse and football teams.
On January 10, 2012, Alosi was hired as the UCLA Bruins strength and conditioning coordinator by head coach Jim Mora.
On June 22, 2015, Alosi was involved in an altercation with rapper Sean "P. Diddy" Combs, over the coach's alleged harsh treatment of Combs's son Justin, who is on the Bruins football team. According to conflicting reports, Alosi either attempted to attack Combs with his hands, resulting in Combs using a kettlebell in self-defense, or Combs attempted to swing a kettlebell at Alosi's head but missed.
Alosi's brother, Pete, is an assistant strength and conditioning coach with the Arizona Cardinals.