Just to be clear, Taiwan did not have huge flows of mainland Chinese soon after the outbreak though. They closed the border to all travelers with PRC passports in mid-February. They did take some drastic measures that have worked.
And before that they had plenty of people coming in from China with active Covid infections - returning from New Year including people from Hubei.
The US enacted their travel ban to China on 31st Jan, yet that hasn’t helped the US...
Now Taiwan is getting cases from other countries (returning citizens and foreign migrant workers) e.g. yesterday: “Meanwhile, the 15 patients deemed to have contracted COVID-19 overseas all returned to Taiwan in the period March 16-23. The countries they had visited were the U.S., the United Kingdom, New Zealand, Spain, Malaysia, Monaco and Mexico.”
Taiwan is still allowing foreign migrant workers to enter the country, as they need them for their economy.
IIRC, most early US cases came from Iran and Italy.
> There are also millions of Taiwanese that either live or work in the PRC
Taiwan has a population around 23.78 million. So you are saying at least 1 in 20 live or work in the PRC...