They indeed shut off foreign travel (not just from China, although that’s a big part of the travel to Taiwan) very quickly. All arrivals must quarantine for 2 weeks, and all foreigners from countries judged to have dropped the ball on COVID control (including the US) must be tested at the airport. In addition, Taiwan hasn’t screwed up contact tracing as we have.
Yes, Taiwan has done a spectacular job limiting the spread of COVID-19. Far better than we have. But they have done it by relying on their citizens to do things that Americans are unwilling to do. If you say the benefits of Taiwan-style measures do not justify the costs in terms of liberty that’s an argument I must take seriously. But anyone who says that Taiwan’s rate has nothing to do with their taking epidemic control seriously is delusional.
You’ll be following Taiwan affairs even more closely if the imbecile that is measuring the drapes for the WH is installed