Unlike smallpox and typhoid and so on, tuberculosis existed in both the Americas and Afroeurasia before the Columbian Exchange. The disease probably made it way to the Americas via infected seals that were butchered and eaten in the Americas, causing people to get TB.
Drinking goat or yak milk can also transmit tuberculosis, although cow milk is by far the biggest culprit.
Sometimes, people even get TB from their aquarium fish!