Wrong Date issues w USB Flash Drive + OS9

I have 2 Ibooks: one has OSX and the other is on the highest version of the old OS9. Something odd happened the other day with a new USB flash drive I started using. I was transferring files (word docs) onto a flash drive. When I inserted the flash drive in the old iBook, each file (and document) showed the date Dec 9, even though the docs were from Dec. 16. When I inserted the flash drive in the newer iBook, it showed the correct dates for each doc. I tried this back and forth, and found the same thing. Yet, all the dates are correct on everything on my hard drive on the old iBook. It only is a problem with this new flash drive I'm using. It never happened before. What could be the problem?