I don't have any firsthand knowledge of this policy, and I'm not sure whether teachers, or at least cram-school teachers, are considered part of the class of "white-collar workers" being referred to when this new policy is discussed, but here's what I've been able to find so far:
forumosa.com/taiwan/viewtopi ... 7&t=133193
The poster quoted above got the extension:
forumosa.com/taiwan/viewtopi ... 2#p1630602
But it appears that he wasn't a teacher when he got it:
forumosa.com/taiwan/viewtopi ... 9#p1676749
Another poster got the extension, but he wasn't a teacher, either:
forumosa.com/taiwan/viewtopi ... 0#p1665260
Here are a few more links about it; they seem to say about the same thing:
chinapost.com.tw/taiwan/nati ... ns-for.htm
ecct.com.tw/news_announcemen ... 6&seq=1174
taiwanease.com/en/forums/nia-kee ... 11460.html
Seeking more details and more certainty--especially about the language used to communicate the class of workers covered--I've visited the websites of the National Immigration Agency (which apparently issues the extensions), the Ministry of the Interior (which apparently made the announcement), and the Ministry of Foreign Affairs (just because their name sounds like this business might have something to do with them), but so far I haven't been able to find anything on those sites. I don't know Chinese, though, so just because I couldn't find it, that doesn't mean it isn't there.
If a teacher has gotten this particular extension, especially a cram-school teacher, it would be nice if he or she would post about it.
As a final, incidental note, apparently the government began talking about doing something along these lines about 2 1/2 years ago, but back then the extension being discussed was for 90 days (again, the term "white collar" is used):
forumosa.com/taiwan/viewtopi ... 7&t=115202
chinapost.com.tw/taiwan/national ... ovt-to.htm
Hope this helps.