Copy/Past object to new document doesn't copy/paste color swatch

I'm having an issue with another employee's computer. They have downloaded the files I need them to work on. I'm having them copy and paste an object with specific color swatches from one file and paste them to a template print sheet file. The swatches show up in the file when opened, but will not copy/paste over to the template file (or any new document for that matter).

The other employee is using a Windows-based PC while I'm using a Mac so I'm not sure if that could be the issue. I've tried installing the Mimaki Rasterlink cutlines plugin, re-downloading the files, and making sure they are using the same version of Illustrator that I'm using. I even loaded the swatches into their Illustrator which added the correct swatches, but when I select the colors on the object that was copied over it's not the same swatches that are in the swatch panel.  It works fine on my end, but not on their computer.

Any help would be greatly appreciated. Thank you.