It can't be an error as that couldn't happen during the striking of the coin. Hard to say exactly how it happened unless you were there at the time but somehow a one cent coin was pressed into the surface either by accident or on purpose. Interested in what others have to say.
That quarter as you mentioned was issued to commemorate Alberta's 100th anniversary of becoming a Canadian Province. There was also one issued for Saskatchewan the same year. These have nothing to do with the the Provincial and Territorial coins (total 12, one issued each month) celebrating Canada's 125th Anniversary of Confederation which were issued in 1992, 7 years before the US Statehood program. The word up here is that the US liked the idea so much, they thought they would copy the idea and issue a coin for each of the 50 states.