Upvote:7
It'll be when you pass through customs. For example, let's say there's an emergency, you get redirected to China for a couple of days, and then flown to Taiwan. They're not going to do it based on your scheduled flight. Indeed, immigration won't usually care what flight you were on or when it was 'meant' to get in - they care that right now, you're standing at their desk and they're approving you for 90 days from then.
However, it's also possible that the shift ends at 1am or something and they don't bother changing their stamps. You could consider dawdling and then asking at the desk to make sure: "This means my visa is from today now, right, given that it's after midnight?". There's no reason they shouldn't, but it may help to 'remind' them that it's a new day.
Of course, real experience on the ground may be a different matter, so if you try it please do report back - it'd be very interesting to hear if it worked.
EDIT
According to Wiki's page on the visa policy of Taiwan:
Citizens of following countries do not require a visa to visit Taiwan for less than 90 days (which starts from the next day of arrival, extension not possible).
and lists countries that fall under this. So it will depend on which passport you're using.