You’re right, they were domesticated in Mexico. Exactly how the turkey was domesticated was not recorded. Recent writers have said that wild turkeys were merely captured, fed and “tamed,” but the wild turkey did not become domesticated by merely being penned up.
The path to domestication likely occurred through the process of parental imprinting of newly hatched wild poults. If wild turkey eggs are hatched in captivity or the young are captured soon after hatching, and the young are allowed to associate only with humans for the first few days of life, the poults bond socially with humans. The bonding is permanent, and thereafter the poults are unafraid of humans and can be raised in captivity. Because imprinted behavior is not heritable, the Mexicans had to imprint successive generations and use only the tamer individuals of each generation as breeding stock. That way, wildness was gradually culled from the breeding pool, and the Mexicans developed a bloodline that exhibited the dependent and trusting behavior of the barnyard turkey we think of as domesticated.
Spanish conquistadores took domesticated turkeys to Spain around 1520, and from there, turkeys spread through much of Europe and the Middle East. The domestic turkey got to England sometime between 1524 and 1541 and to the English Colonies in North America not long after that.
The wild turkey indigenous to the eastern United States has never been domesticated, although Easterns have been crossed with domestic stock to produce a breed tame enough for captive rearing.
— Lovett Williams, 2013