Coming out of the AC Milan Youth Academy, Evani was promoted to the senior team, where he developed into technical fast left-sided midfielder. He made his debut in 1981 at the age of 18, going on to wear the Rossoneri shirt for the next thirteen years. Although he was not as quick or as talented as some of the more prominent players in Milan at the time, the quality, work pace, and flexibility of Evani along the left wing proved vital to the Milan senior team, especially under both Sacchi and Capello.
With Milan fans, “Chicco” will be mostly remembered for scoring the winning goal against Atlético Nacional in the 1989 Interncontinental Cup final. A left footed freekick in the last minute of extra time that left Higuita staring and Galliani sprinting to the middle of the pitch with joy. However, he also won the following trophies, 2 Serie B promotions, 3 Serie A Scudettos, 2 European Cups, 2 Italian Super Cups, 2 European Super Cups and 2 Intercontinental Cups.
Following his retirement, Alberico coached the Milan under 17s and won the national championships in 2007. Later on, he managed the Italian National squad’s under 18s, 19s and 21s for few years. In 2019, Alberico published an auto biography titled "Non chiamatemi bubù".