I'm not sure what my expectations would be if after copying files to a drive I then use a backup program to copy them over. I'm not trying to worry you, it is just that the two processes most likely follow different rules. If your plan was to overwrite all of the files on your external drive, it probably doesn't matter. It appears that the program in its simplest form is just doing a file copy, so you should be okay. But back to you question... A program has multiple ways of deciding which files to copy and when. If the program is grabbing the file names directly from the File Allocation Table and not sorting them in any way, then the order of files will be different than what you are looking at when you look at your folders. If the program is not backing up files because they exist or they are newer, then you might not see them on whatever list is showing up. Hopefully the program gives you a nice big log so you can verify it is doing what you want.
My master files are not kept on my "media server". So, I do a copy every night using Microsoft's SyncToy. It's a free app, pretty easy to use and doesn't overwrite newer files. I also use it for my car. I have flash drives that I take into the car. If the drive is not in my computer, SyncToy just ignores the backup process.
I hope something in here helped.