Evison burst on the darts scene in 1986 with a surprise victory over John Lowe in the British Professional Championship, a major televised tournament in that era.
Evison made his World Championship debut in 1988, and went on to reach the quarter-finals, before losing to the eventual champion, Bob Anderson.
Evison had a dip in form at the World Championship between 1990 and 1992, failing to get to the quarter-finals in any of the three, despite a first round win over John Lowe in 1991.
Evison reached the semi-final of the inaugural 1994 PDC World Darts Championship losing to eventual champion, Dennis Priestley.
Evison failed to pass the first round of the 1999 World Championships, but reached the quarter-finals again in 2000 – losing this time to Peter Manley.
He managed one preliminary round win in 2005 at Purfleet, before being badly beaten in a grudge match against Andy Jenkins.
In 2008, it was announced that Evison was one of eight players to take part in the BetFred League of Legends alongside the likes of Bristow, Bobby George and Lowe.
Evison took part in the BDO International Open on 15 June 2008, receiving a bye into the second round before losing to Paul Hanvidge 3–2 in legs.