Tsai and her independence-leaning Democratic Progressive Party (DPP) won presidential and parliamentary elections by a landslide on Saturday, prompting concern in Beijing that she may push for the island's formal independence.
As of Thursday morning, more than 40,000 people had made comments on her Facebook page, in a repetition of a similar incident in November.
Many of the posts were written in the simplified Chinese characters used on the mainland, and a lot of them repeated a standard Communist Party refrain about how shameful it is to harm the motherland.
"Why do Taiwanese think we've all been brainwashed? We've all be taught from small that Taiwanese are compatriots, and Taiwan is the jewelled island," wrote one, apparently Chinese, poster.
Others referred to Tsai as "Taiwan province governor".
"Absolutely Taiwan is part of China unless you are taught in a misleading way," one person wrote in English.
Facebook is blocked in China, though there are ways round it even if most Chinese people don't have access to that technology.
DPP spokesman Ruan Chao-hsiung said Chinese internet users were just "exercising their freedom of speech".
"As long as their comments are not overly extreme, we have full respect for them," Ruan said.
Tsai herself posted on Thurday: "The greatness of this country is that everyone has their own rights".
Tsai says she wants to maintain peace with China, as well as the current status quo. China deems proudly democratic Taiwan a wayward province to be taken back, by force if necessary, particularly if it makes moves towards formal independence.
Taiwanese reacted to the Facebook barbs, offering sarcastic congratulations to Chinese that they were able to escape their government censors and use Facebook freely, and pointing out the freedoms people in Taiwan enjoy that in China they do not.
"We have freedom of speech, freedom of assembly and personal freedom. You people have none of that," wrote one.
China's Taiwan Affairs Office did not respond to a request for comment.
Chiang Kai-shek's Nationalists fled to Taiwan after being defeated by Chinese Communists in a civil war in 1949. The island has been self-ruled since.
