This happens because Photoshop latches on to whatever EXIF date it can find when importing JPG images into a PSD (e.g. drag/dropping references).
Photoshop will export whatever EXIF date it has laying around into the final JPG. This is incorrect program behaviour. The EXIF date of my reference images has nothing to do with the image I'm producing. No PSD file should ever produce EXIF data on export, unless prompted to fill out such fields at the time of export.
Windows Explorer is working as intended. Stop telling people to "Sort By Date Modified". The "Sort by Date" column is intended to sort by EXIF date when available.
Users: The correct fix for screwed up JPG date sorting of your images?
Manually alter the EXIF date. Right-click the file that was exported with bugs --> Properties -> [Details] -> "Date Taken" field.
Or, open your references in MSPaint (lol), copy the image to your clipboard, and then paste it rather than drag / dropping it in.
Or, don't use JPG.
I'm not clear on all the exact conditions that trigger this, but it's definitely been happening silently as I drag-drop images into a PSD. I'm also not paid to test Photoshop, so you'll need to repro yourselves.
If Adobe staff cannot reproduce the problem, then it means your developers are relying on some sort of intermediary 3rd-party library / dependency that's doing something wrong. Still a Photoshop bug / incorrect program design -- sorry, can't defer :). This bug has existed for 5 years and every thread asking about it is an exercise in pain.
See attached properties dialog. I made this image today, yet it popped out with an EXIF date from over a year ago because I painted over some references that were imported as JPGs.