Some of the dialects came from the mainland....others of the more indigenous types are a bit different.
Honestly though I would have to brush up on the Taiwan linguistic thing...pose some questions and I will try to look up some answers if need be. I have not lived on Taiwan ever so I honestly have limited exposure to the minute differences in linguistics.
Some people say the real native language came from a Melanesian background (island people)...I have also heard people make connections with sea faring peoples named in ancient Chinese texts who were used as servants.
For a real solid answer as in yes or no its hard to say...there is no difinitive answer as far as I know unless something recent has been uncovered.
Much of the "Taiwanese" you're probably talking about though came due to migration.
I was just curious about its history. I spent a year in south Taiwan. Nearly everyone speaks Taiwanse. My wife is a native Mandarin speaker and couldn't understand much of it at all. Natives down there also speak something called Hakka, which is different from Taiwanese. It's interesting because the government can't quite decide which language they want children learning in school--Mandarin, English, Taiwanese, or Hakka (for the natives).