The quick answer to your question is yes, Native Americans indeed were the people that originally domesticated turkeys. Then, European explorers took the domesticated bird with them back to Europe where it became a sensation that spread to the rest of the world. However, where exactly did turkeys were domesticated is still a bit of a mystery, primarily due to the lack of work on the subject. While it has been suggested that turkeys were originally domesticated in central Mexico, given the presence of bones in archaeological sites dating to around 800-100 BC, studies in the North American Southwest (around the Four Corners Area) suggest that Pueblo ancestors may have also domesticated turkeys separately from their Mesoamerican counterparts. This would imply at least two domestication episodes, but given the problems of identifying wild turkeys (Meleagris ocellata) from the domesticated variety (Meleagris gallopavo), it is difficult to securely assess the timing of the domestication of the specie. Suffice is to say that by the time Europeans arrive to the Americas, domesticated turkeys had become an important part in Native cuisines.