Yugoslavia was not created until the end of WWI. He would have been born in the Austro-Hungarian empire.
I did find a marriage for a Peter Culumovic in Sudbury in the parish records of St. Trinity, born December 1915 in Croatia; names his parents as Gregory Culumovic and Mande Urimovic; dated March 12, 1949. He may be a brother or a cousin to your Stephen.
The passenger record for Stjepan indicates he was born in Prvanselo, Yugoslavia; naturalized on 15 April 1931 (Registration #415743); gives his wife, Manda in Prvanselo as his next of kin at home. Says he was bound for Winnipeg.
From the same village, there is a Marko who arrives in 1928, also bound for Winnipeg; gives his wife, Mare, as his next of kin at home.
Also in 1928, a Mile, born 1895, arrives, also from the same village, also bound for Winnipeg.
In 1936, I find Manda (see wife of Stjepan above) arriving in Canada, arriving through the US, bound for her husband Stike (?) in Port Colborne, Ontario.
Alexander may have ended up in Rouyn, Quebec, where I find baptisms for his children in 1936.
I did find a death record for a child, Mary, of Steve Chulumovich & Rose Smith, aged 26 days, in October 1938 in Sioux Lookout.
Alexander and his wife show up in Timiskaming in 1933 with the death of a child, George Victor, aged 18 days; informant is the mother of Rouyn.http://www.canadianheadstones.com/on/view.php?id=106362
There is an online tree at Ancestry.ca giving Stephen's birthdate as 9 November 1900 in Lika-Senj, Crotia; died in 1974 in Sioux Lookout. From that tree, it would seem that only one of the children changed the name to Chumm; others retained the Chulumovich spelling.