Taiwan was pulled into the Chinese cultural sphere only in the last millennium. At the beginning of the study period it was inhabited by the aboriginal Taiwanese, and may be the point of origin for the Austronesian conquest of the Pacific.
Fifteenth Century: The Chinese begin to settle on Taiwan. (During the Ming Dynasty that took control of China after the collapse of the Mongol Empire.) If your ancestors were Han Chinese on Taiwan in CE 1490, their ancestors probably lived both on Taiwan (as native Taiwanese) and in Eastern China in CE 1000.
Sixteenth and Seventeenth Centuries: Portuguese, Dutch, and Spanish colonists wrestled over Taiwan. If you are of Taiwanese extraction and look oddly European, it is possible that you had European ancestors in CE 1490.
1660: Fleeing the invading Manchus, remnants of the Ming Dynasty take refuge in Taiwan. Soon, the Manchus show up and incorporate Taiwam into their Qing Dynasty. The Qing government opened Taiwan up to extensive Chinese settlement. If your ancestors were ethnic Chinese in Taiwan in CE 1800, their ancestors probably lived both on Taiwan (as native Taiwanese) and in Eastern China in CE 1490.
1895: The Japanese conquer and administer Taiwan until 1945. If your ancestors were in Taiwan in CE 1900, it's not impossible that they had ancestors in Japan in 1800. Look to your family folklore for info.
1949: The Kuomintang government, fleeing the creation of the People's Republic of China, landed in Taiwan just like their Ming Dynasty predecessors. Many people immigrated from China to Taiwan at this time. If these are your ancestors, family folklore will tell you.