As others have now stated below, you are correct that Manitoba records are in Manitoba. One other point - records may also be found among the Hudson Bay Company Archives (it was founded in 1670) in Winnipeg, and also at the National Archives in OTTAWA.
Another point - Manitoba [ the part south of the lakes ] actually became a Province in 1873. The northern 80% of it, which was added later, was called the North-West Territories along with the north of what is now Saskatchewan and Alberta, and the current NWT and Nunavut (noo-nah-voot).
The southern part of Sk and AB were called Rupert's Land at this time in history. SK and AB only became provinces in 1905. British Columbia on the Pacific had been a province since 1871 (they joined after Ottawa promised a railway connection right away - the train finally arrived14 years later).