Born in Belgrade's urban neighborhood of Dorćol, Tumbaković started out in the youth categories of Radnički Beograd in 1962.

He would stand down from his position after almost a decade in charge of FK Partizan where he was one of the most successful coaches in Yugoslavian football history.

However, he quickly moved to Chinese team Shandong Luneng at the beginning of their 2004 league season.

Tumbaković who was the second Serbian to manage Shandong after Slobodan Santrač, was to make a quick impression at the club when he won the Chinese FA Cup and took them second in league.

Tumbaković was appointed head coach of the Montenegro national team on 19 January 2016 and was sacked on 7 June 2019[8] after refusing to take charge of a UEFA Euro 2020 qualifying game against Kosovo and abandoning the staff on the match day.