a hard question – as many minhagim may be influenced by cultures we lived in. One example from the Torah would be Hashem insisting on hatzot for yetsiyat Mitzraim – and following up on his threat. So, apparently, He considers important to follow up the time, even when the other side does not insist on it. In other cases, “boker” or “erev” seems to suffice.
Maybe, the bottom line is that you don’t have to go crazy about timing. Asa Avira is saying, depends on the person. One may need a precise schedule, another can dedicate an afternoon to a topic… but if you did make an appointment or a schedule, then you should follow up.
Note that computer culture promotes the Yekkesh attitude: taxes are due until 12:00, same goes with online exams and proposals. Is it the same everywhere or just in US? Do online systems in South America allow for late returns?