Robert Langdon, in "The Banana as a Key to Early American and Polynesian History," Journal of Pacific History 28, no. 1 (1993): 15-35, pointed to a lack of consensus on this question, although it's very likely the matter has moved in the last twenty years. The question is whether it came via Southeast Asia (in Langdon's particular view, about two thousand years ago, after which it secondarily spread back into Polynesia from Ecuador perhaps with the sweet potato) or whether it came west with Iberian expansion and raced ahead of it after landfall. In 1993 the matter was not clear. If there's now agreement on dates of transfer and mechanisms/locations I'd like to know as well.