Why does the file date always change to the current date?

"First I agree with th3dude19 - check whether or not it's happening in regular Explorer as your first step.

If it's still being modified, then if you have Anti-virus it may be re-dating (modified date) the files as it scans them (during the move to the new drive).

This isn't usual, but I've run into it (in that case it was causing an automatic off-site backup to resend files that hadn't changed in any other way).

So try disabling your AV and see if the date sticks as expected."

Process Monitor can indicate unwanted modifications to files.