Jaso graduated from McKinleyville High School in McKinleyville, CA in 2001. He then attended Southwestern Community College in 2003 and was then originally drafted by the Tampa Bay Devil Rays in the 12th round (338th overall) of the 2003 Major League Baseball draft.
Jaso began his professional career playing for the Low Single-A Hudson Valley Renegades for two seasons from 2003 to 2004. He had a .221 batting average in 2003 but improved to .302 in 2004 and was also a postseason All-Star for that season. He took the next step in 2005, playing for the Single-A Southwest Michigan Devil Rays. He had a .307 batting average and had 14 home runs, his most of any season to date. Also, he was a midseason and postseason All-Star. In 2006, he took another step, playing for the High Single-A Visalia Oaks and his season included being named to the midseason All-Star team. In 2007, he played for the Double-A Montgomery Biscuits. His .316 batting average was second in the Southern League, on base percentage of .408 was third among league leaders and a slugging percentage of .484 was good enough for sixth in the league. His best minor league season included being named to the midseason and postseason All-Star team and was also Topps Southern League Player of the Month for August. Baseball America and Topps also named him as a Double-A All-Star after the season.