[2] Vinčić went to UEFA Euro 2012 as additional assistant in the team of Damir Skomina.

Additionally, Vinčić refereed the 2024 UEFA Champions League final at Wembley Stadium.

He was also the referee for the 2022 UEFA Europa League final between Eintracht Frankfurt and Rangers.

On 30 May 2020, Vinčić was arrested by mistake as part of a police probe into a prostitution and drugs ring in Bosnia and Herzegovina[3] but was soon cleared of any wrongdoing.

[5] On 24 February 2025, he refereed the Turkish Super League fixture at Rams Park between Fenerbahçe and Galatasaray.