Wines played his junior football at the Echuca Football Club and for the Bendigo Pioneers in the TAC Cup before being drafted by Port Adelaide in the 2012 AFL Draft. Wines' great uncle was Clinton Wines, who played 39 games for Carlton from 1945–1946, including the "Bloodbath" 1945 VFL premiership.
Prior to the 2012 AFL draft, Wines was predicted to go to the Melbourne Football Club along with Jack Viney, his best friend who attended the same primary school at Echuca and was already a father-son selection pick with Melbourne. Instead he was overlooked by Melbourne and was drafted by Port Adelaide with their first selection, pick seven, in the 2012 national draft. He made his AFL debut in the opening round of the 2013 AFL season at the Melbourne Cricket Ground against Melbourne, which also featured his best friend, Jack Viney. Port Adelaide won the game by 79 points. In an impressive debut, Wines finished the game with 24 disposals including 16 contested possessions and one goal, earning him the round 1 nomination for the 2013 AFL Rising Star. He ended up finishing third in the Rising Star with 26 votes.