Minasian grew up in clubhouses thanks to his father, who was a clubhouse manager for the Texas Rangers for over two decades. The four Minasian boys helped out on the visiting side, watching great players like George Brett, Ken Griffey Jr., and Robin Yount. They unpacked equipment trucks at four in the morning and then went to school. One brother became the GM of the Los Angeles Angels, and another worked for the Atlanta Braves. Minasian said, "The understanding was you can come in this clubhouse, but you have to work. I probably broke a lot of child labor laws, but I loved every minute of it."
When their father moved to the home clubhouse, they celebrated wins with Rangers players. But the long seasons taught Minasian a lesson. He said, "I don't know if I got addicted to winning as much as I just hated losing." These lessons stayed with him when he went to Milwaukee, where he spent 14 years and became the youngest pro scouting director at 27. He was instrumental in helping the Brewers acquire CC Sabathia and Josh Hader. In 2010, he made a deal with his brother Perry that had its roots in the 2008 MLB Draft.
Minasian was hired by Farhan Zaidi in 2019, a crucial step in his career. His grandfather and father were close to Tommy Lasorda, who became his godfather. When he got hired, Lasorda called him Benedict Arnold. Three years later, he was promoted to VP of pro scouting. Two years after that, Posey chose him as his partner during a crucial period. Minasian views his pro scouting background as preparing him for this role. He said, "It's funny, people talk about rising from the bottom. I never viewed working in that clubhouse as the bottom. It was a privilege."