First of all, look at the tell tale sign on the death number of Taiwan, Vietnam, Thailand and China who were able to put the pandemic under control for a long time. Then you see at some point, Taiwan, Vietnam, Thailand started to have death number gradually increasing until it spike. China is now the only one able to keep the pandemic at bay. Taiwan and Thailand's trouble probably started at the beginning of this year, but since many are asymptomatic, they managed to hide it with limited testing, until death started to pile up. Thailand's death started to jump in early Apr, while Taiwan's in mid May. From here onwards, they couldn't cover it up anymore.

As of May 26, 34 of 46 death occurs after May 15. This is what the daily cases look like without the so called "backward adjustment". Using the 7 day average is a better indicator than randomly patch up numbers.

As of May 25, at least 7 of the death happened outside of hospital, 3 died before they were confirmed as Covid-19 death. This means there're community spread before the Taiwan MOH even realized it with their inadequate testing.

As for how did the virus get into the country. Taiwan is not as isolated as you think. Taiwan airline pilot contracted B.117 variant in UK, flew back to Taiwan only need to self quarantine for three days. Then he visited the red light district to do "people to people connection" and become a superspreader. People in the red light district then hide it for over a month. Many Taiwanese repatriate from India may also carry the virus.