It was not until audience pressure concerning another representational faux-pas forced the production team to write a specific tribal heritage into the character that this generic Indian-ness was specified.
This second faux-pas concerns the actor casted to play Chakotay. Robert Beltran is Mexican American, and although he tried to justify his playing an “Indian” role by evoking the Mestizo heritage of many Mexicans, many viewers experienced his presence as “yet another non-Indian actor [...] in a part that is identifiably Indian and uses trappings from the culture.” Only very gradually, and at Beltran’s own suggestion, did the producers effectively solve the problem of their own casting decision by specifying Chakotay’s tribal affiliation as “south of border”, i.e. Mayan, Aztec or Inca.
Imagine saying the character could be Lakota (nomadic warriors), Hopi (peaceful farmers), or Maya/Aztec/Inca (empire builders). Because all Indians are the same, right? If they're not savage fighters, they're wise spiritualists. Chakotay started out as the former (a Maquis resistance fighter) but quickly became the latter.
Yes, Chakotay was a typical generic Indian, all right. Voyager eventually established that he belonged to the fictional "Rubber Tree People" of Central America. Fictional tribes are bad enough, but the show revealed that the tribe's "Sky Spirits" were--wait for it--space aliens. Once again, "primitive" Indians are unable to accomplish anything on their and must get the help of extraterrestrials.
For more on the subject, see The Indian-Star Trek Connection.