My guess, from looking at your picture, is that probably GIMP holds the EXIF metadata in memory, and that it
automatically gets saved whenever you save the GIMP .xcf file, and gets exported along with the image
whenever you export as an image format that can save EXIF metadata, which I think is just .jpg and .tiff.
"It is not used in JPEG 2000, PNG, or GIF."
[As an aside, possibly relevent:
I had the situation, that when I renamed my photos, or rotated them in an image-viewing program, or
possibly also overwrote them in GIMP, that the file-modification date/time became the day that I renamed/
rotated/overwrote them, and that because I needed the file-modification date/time to remain the moment
that I took the picture (primarily for ease in sorting through the photos in Nautilus/Nemo - so that I could tell
what pictures were taken after what other photos, and what were all on the same date, etc.), I needed some
way to change the date/time back to the original photo-taking time.
I google'd the issue, and found that I could use the following command to reset the date/time to the original: