Frogboy: Perhaps "Royalists" is the American version of the term "Loyalists", which refers to those loyal to the British crown. I don't know.
The immigration of Loyalists to Canada continued long after the American War of Independence, however. If memory serves this issue was involved in the War of 1812, which was itself fought largly over issues of conscription.
As for what does and does not constitute a tradition, who cares? My point stands whether this was a tradition or just something Canada did a couple of times. I doubt whether you think Canada should be accepting U.S. draft dodgers (or those who aren't given a fair hearing when it come C.O. status) is really gonna rest on how often Canada has done this in the past.