jegsav (or within a second or two of [end time])
Yep, it is not even precisely at the end of exposure time on ASIAIR. This is what I see in an ASIAIR FITS header:
DATE-OBS= '2021-06-29T08:24:08.310' / Image created time
It is the time the image was written out (so it includes time spent to download the data from the camera, generate the correct format, the headers, etc). You cannot depend on it even as the actual end of the exposure time, even if it is stated to 1 millisecond.
On the other hand, the latest version of ASIImg created a FITS file that says:
DATE-OBS= '2023-02-10T09:30:01.877' / UTC start date of observation
But I can confirm that it is not the start date. It is also not the end time, but like what you said, a couple of seconds later. I suspect it, like the ASIAIR case, is also the time when the file was created.
Not even the time when the image was created, as the ASIAIR claims. (I suspect the downloading time takes up most of the difference.)
Chen