Transferring file creation dates to an Asustor NAS
The Problem lies not in your Asustor per se but in the file system (and subsequently the drive configuration) you use and the copy routine you use. In a nutshell: There are different methods to copy files (f.e. rsync) and different ways the file systems store data (f.e. creation date). 

Without further Information regarding your NAS-Setup, File system (necessary) and RAID Level (not necessary, just to be complete), the possible solution at this point would be very general: One possibility would be to use rsync to transfer files from you Mac to the NAS - it should copy all data including creation date. It is a command line tool but there is Software with a GUI which should be more to your likeing. I suggest 'Carbon Copy Cloner', a commercial software but with a 30 day trial.

You should start with that and test it with a few files. If it does not work you should provide more information about the file systems used in the NAS and your external drives.