Ashtone attended Northern Secondary School in Toronto and played for the Toronto Lynx U-13 squad that travelled to England to play other youth academies. On this trip he was the standout player of the Canadian side earning him invitations from clubs such as Southampton.
Morgan joined TFC Academy at age 16 in 2008, and went on to feature for the team in the Canadian Soccer League in 2009 and 2010. Morgan made his professional debut for Toronto FC on October 20, 2010 in a CONCACAF Champions League match versus Árabe Unido from Panama. Morgan was able to play for the Senior squad of Toronto while not holding a professional contract. The game ended in a 1-0 win for Toronto with Morgan having a stand out performance that earned him much publicity. In late January 2011 it was announced that Morgan would travel with Toronto's Senior team to Turkey for preseason training camp, Ashtone was one of four academy players invited to travel. He signed with Toronto FC on March 17, 2011. Morgan made his league debut on March 26, 2011 against Portland as a second half sub for Javier Martina. In the last third of the season Morgan became a regular starter for the reds with playing a full 90 minutes in 7 of the last 10 league games. Morgan finished the 2011 season with 14 league games. Morgan cemented himself as the starting left back for Toronto in the 2012 season, he registered 3 assists in two games in late June. On July 5, the club announced that it had re-signed Morgan to a long term deal.
However, with the arrival of Justin Morrow, Morgan saw his minutes decrease during the 2014 MLS season, mainly featuring as the club's back-up option at left back. With Morrow entrenched at the position going into the 2015 season, Morgan was loaned to Toronto FC II to get more playing time, while still being able to feature for the first team when needed. He made his debut for Toronto FC II against the Charleston Battery on March 21. However, with injuries to the first-team back line, Morgan was able to force his way back into the Toronto line-up during the 2015 season, and on May 2 he became the first player in Toronto FC history to make 100 appearances in all competitions for the club in a 1-0 victory over the Philadelphia Union. Despite missing the majority of the 2016 season due to injury, as Toronto FC made it to the 2016 MLS Cup, Morgan relished the club reaching its most successful season to date. Upon completion of the season, Morgan re-signed with Toronto FC before the 2017 season. Toronto declined his option for the 2020 season, ending his time with the club after nine seasons.
