Currently it seems that the modification dates of all files in artifacts are reset to 1970-01-01T00:00:00Z (Unix time 0). Here's an example artifact for instance.
It seems that the archives are created using something like
tar --owner=root:0 --group=root:0 --mtime='UTC 1970-01-01'
This causes side-effects downstream, which I can't really blame Bitbucket on though, e.g. Adobe Reader loading outdated cache. I'm not sure what the motivation behind is but for me it'd be nice to have a straightforward approach to tackle this.
PS: I've found a Bamboo issue that looks rather similar https://community.atlassian.com/t5/Bamboo-questions/Keep-original-timestamp-on-build-artifacts-during-artifact/qaq-p/295379