Volstad played in amateur baseball tournaments from a young age, winning the championship in a 12-and-under travel competition for a team representing Broward and Palm Beach counties, against a team representing California's Central Valley, at the Baseball Hall of Fame in Cooperstown, New York.

[1] Volstad graduated from Palm Beach Gardens Community High School in 2005, pitching to a 7-2 win–loss record with one save and a 0.41 earned run average (ERA) in 10 games for the school's baseball team as a senior, striking out 98 batters and walking just eight in 69 innings pitched.

Volstad never returned to Jamestown, instead starting out 2006 with the Greensboro Grasshoppers of the South Atlantic League (Class A).

Volstad started his second full pro season with the Jupiter Hammerheads of the Florida State League (Class A-Advanced).

However, in later action with Florida's AA affiliate, the Carolina Mudcats of the Southern League, he improved to a 4-2 record and a 3.16 ERA.

In 2008, Volstad continued at Carolina, posting a 4-4 record, 3.36 ERA in 15 starts before being promoted to the major leagues.

He made his major league debut the same day in a game against the Colorado Rockies, earning the win with 2 scoreless innings from the bullpen.

Volstad added his first major league hit in this game: a single off the Dodgers starter Eric Stults.

On August 7, 2008, Volstad delivered a masterful performance against the NL East-leading Philadelphia Phillies to reduce their lead in the division to 1+1⁄2 games.

Against the San Francisco Giants, he pitched his first career complete game allowing only five hits and no runs.

In late August 2009 he was sent to the Triple-A New Orleans Zephyrs[4] after a 1+2⁄3 inning start against the San Diego Padres.

Morgan proceeded to steal two bases when the Marlins had an almost double digit lead, breaking an unwritten rule of ethics in the game.

[16] Then, after pitching in relief for two scoreless innings in a game on June 24, 2015, Volstad was designated for assignment alongside José Tábata on June 28 to make room for Gorkys Hernández and Steve Lombardozzi Jr., he cleared waivers and was sent outright to Triple-A Indianapolis Indians on July 2.

[18] On March 24, 2016, Volstad signed a minor league contract with the Chicago White Sox.

In 29 games (27 starts) for the Triple–A Charlotte Knights, he compiled an 8–11 record and 4.79 ERA with 84 strikeouts across 176+2⁄3 innings pitched.