If you want a creation date to reliably accompany a file you need to either 1) add the tag EXIF:DateTimeOriginal with the proper date value to the file’s metadata, or 2) incorporate the creation date/time into the filename itself.
exiftool can aid you in doing either of these:
It’s a command line program, and there are GUI shells available for it. Of note to your specific need, there’s also an EXIF:Copyright tag available for you to insert your copyright assertion.
The operating system file date/times do not behave to the rules we photographers cherish…