I have been informed from an aberdeenshire person that Old Don was a part of the old town of Aberdeen
Well, I have to admit that even when I lived in Aberdeen I never heard the term "Old Don". Even the bridge is 'Auld
Brig o' Don" and the area around it is "Bridge of Don". More to the point, if he was born in Old Aberdeen, the name of the parish of his birth is Old Machar, not Old Don.
The 1881 census records
Alexander Robertson, aged 10, born Old Machar, mother Jane (father not in huosehold)
Alexander Robertson, aged 11, born Old Deer, in the parish of Deer, parents Alexander Robertson and Eliza
Alexander Robertson, aged 12, born in Old Machar, parents James and Mary
Alexander Robertson, aged 12, born Old Machar, son of a widowed Donald
There are several others aged either 10 or 12 born in Aberdeen with no indication of which parish, and one more born in Belhelvie an living in Old Deer.
There is something odd about the 11-year-old born in Old Deer; I cannot find his birth or those of his siblings in the IGI, which is unusual for 1870ish.