Thus, to chime in for a moment as the resident Japanese historian in the department, I want to make clear that the word "tobacco" does indeed date back to the late sixteenth/early seventeenth centuries in terms of its usage in Japan. It is not found among the words listed in the first major Japanese-Portuguese dictionary published around 1600, the Vocabulario Da Lingoa De Iapam, probably because it was not a "foreign" word to the Jesuit missionaries who compiled this text. But the word "tobacco" is attested to elsewhere.
One good example comes from an early seventeenth-century law code issued by the Uesugi family (上杉氏), the daimyo in charge of Yonezawa domain (米沢藩). The code, promulgated in the eighth month of 1612, contains an article that states the following:
"It is strictly prohibited for those serving under a lord to smoke tobacco in the courtyard of his residence." (たばこ．．．主人の供仕、門庭において飲候事、一切停止之事)
A couple of points about this passage and the larger code:
1) "Tobacco" is written in hiragana.
2) The verb that is used together with tobacco here is nomu (飲む).
3) The remainder of the law code also makes clear that one is additionally to refrain from smoking around both the sick (病者) and the elderly (老人).
It therefore seems likely that it was indeed the sound of the word "tabaco" in Spanish and Portuguese that was first converted into hiragana before various ateji (当て字), or variants, using kanji were assigned/invented thereafter.
It is also probably worth noting that, back in 1612, there were already lawmakers who realized that tobacco is bad for your health...
