The Copy Files action uses the CopyFileEx API to copy files, which sets the creation time to the current time and retains the modification time of the original file. This is consistent with copying from a command prompt or Windows Explorer, and retaining the modification time value is necessary to support incremental file copy.
After copying, you could use a touch utility (such as the one in
http://unxutils.sourceforge.net/) to modify file timestamps. We'll consider adding an option to the Copy Files action set the created/modified timestamps for all copied files to a user-supplied date/time value.