We've all been side-tracked by family folklore.Don't despair (my uncle swore to his deathbed that his grandmother was a debutant from NY with an extensive royal pedigree...she was really a farm girl from Beaver Twp, Bay Co. Michigan who died young...as did almost all of her kids...leaving a bunch of young grandchildren whose imagines threw the slightest details out of proportion.)
Reality is that there was SO MUCH land, and so many people all having the same surname, there was no need to change his name when he came to the US.He may have done it to set himself apart from a large contingency of relatives, or to please a wife who didn't like spelling a difficult French name for a bunch of idiotic American bureaucrats.Maybe it was a spelling mistake that just took hold and no one fixed it.Or possibly he just liked Casey better than Tessier and adopted it.The US and Canada had such an incestuous relationship for so many years, that the Canadian law wouldn't have been a major worry once they got here.
Here's a decent synopsis of Canadian history.
c. AD 1000 Vikings, including Leif Ericsson, landed in northeast Canada, and started settlements that did not survive.
1497 John Cabot landed on Cape Breton Island.
1534 Jacques Cartier reached the Gulf of St Lawrence.
1603 Samuel Champlain began his exploration of Canada.
1608 Champlain founded Quebec.
1755 French Acadians of Nova Scotia were exiled from Canada in "Le Grand Derangement."
1759 James Wolfe captured Quebec.
1763 France ceded Canada to Britain under the Treaty of Paris.
1775–83 American Revolution caused Loyalist influx to New Brunswick and Ontario.
1791 Canada divided into English-speaking Upper Canada (much of modern Ontario) and French-speaking Lower Canada (much of modern Quebec and mainland Newfoundland).
1793 Alexander Mackenzie reached the Pacific by land.
1812–14 War of 1812 between Britain and the USA. US invasions repelled by both provinces.
1837 Rebellions led by William Lyon Mackenzie in Upper Canada and Louis Joseph Papineau in Lower Canada.
1840 Upper and Lower Canada united to form the Province of Canada.
1867 British North America Act created the Dominion of Canada (Ontario, Quebec, Nova Scotia, and New Brunswick).