Being punctual is very important for teachers – because students are often even more punctual and are waiting for the teacher to arrive! Punctual in its most common use means the ability to arrive ‘on time’. So if someone says they will be there at 8am and they arrive at 8am, they are very punctual.
The word does have a link to being strict or detailed but it is not commonly used this way, and therefore often appears wrong when used in English. If you wish to say that someone is very detailed and doesn’t make errors, instead of using the word ‘punctual’, you should use the word ‘exact’, ‘precise’ or ‘accurate’.
Here they are together:
A: He never gets any details wrong. He’s so precise.
B: Yes he’s certainly accurate in his work but one bad thing you can say about him is that he’s definitely not punctual. Yesterday, he was 40 minutes late to our meeting!