The FITS “standard” is irritatingly vague about things like this and, particularly for astrometry, it is really important to know what DATE-OBS means. In most software these days it is the time that the exposure starts but sometimes it isn’t. In “good” software there is often a comment along the lines of:
DATE-OBS= ‘2021-07-26T22:03:10’ / Start of exposure
but often there isn’t and so it is always worth checking for whatever image acquisition and processing software you use.