This looks right for 1916 although surname spelled wrong, but that is not unusual.
1916 O5, MACKENZIE, SASKATCHEWAN
Adam, age 30, farmer, born Hungary, immigrated 1907
Julie, age 26,wife, born Hungary, immigrated 1907
Alex, age 8, son, born Canada
Annie, age 6, daughter, born Canada
Frank, age 4, son, born Canada
Andrew, age 2, son born Canada
Joe, age 2/12, son born Canada
This was the only family I found in 1911 that seems to fit at all, but it does not agree with what you have as to them immigrating in1903 BUT names and ages fit pretty closely except wife is shown as Simona, not Julia
1911 MACKENZIE, SASKATCHEWAN
Adam, age 25, farmer, born Jan. 1886 Hungary, immigrated 1906
Simona, age 20, wife, born March 1891 Hungary, immigrated 1906
Alexander, age 2, son, born Dec. 1908 Sask.
Annie, age 7/12, daughter, born Oct. 1910 Sask.
You mentioned that they homesteaded - have you sent for their homestead records? If not, I think you can get them through the Sask. genealogical society - at least you used to be able to
The only other thing I can think of for you to find when they went to Bernard and when they left would be to check for land records - purchases and sales or foreclosure as you suspect.Perhaps the town records office could help you or the provincial records office.