WHy am I getting .DMS files?

If you have a shared network, open up a file share on one or both systems, and you can drag and drop to the other system.

 > System Preferences > Sharing > ☑️ File Sharing, and then you can specify paths you want to export, and mount the export over on the other system, and can then drag and drop files as needed.

If you're inclined, you can open up your main login directory as a share, and drag and drop files to and from there.

if your Macs are new enough for it, AirDrop can also work for local file transfers, though—for specifically what you're up to here—a file share will work much better.

Mail is All Sorts of Bad, when copying files around. Mail servers can do all sorts of shenanigans with attachments, contents, sizes and the rest of filing and filtering and storing. Please don't use Mail as a file distribution mechanism. It's really designed and built for mail. Not for shipping around parcels.

Mail servers can do weird stuff with mail, as they're often configured to block spam and malware, to block attempts to DoS folks by shipping them large files, and these among other site-specific and server-specific requirements.

There's a very long history of folks trying to misuse what is effectively a letter delivery service for a parcel delivery service, and the results aren't always as expected.

Open the shares. It's a much better solution for shoveling files around within a house or within an organization, and you're not sending what can be larger files up and down your external network.

Various homes with lots of computers and many organizations will end up with network-attached storage boxes ("NAS"), and which the local systems can access and can use to share files and data. Or with installing local cloud-hosting approaches, such as OwnCloud or NextCloud.

Can you confirm DMS? (Not DMG? That DMS type is fairly rare on Mac; Amiga was one of the few environments that used DMS.)

Can you describe how are you transferring files to your computer upstairs, and what apps or tools you're using?

What sort of computer is the upstairs computer? Another Mac? Windows?

Is there a network available between these computers, or are you using a USB device such as a flash drive to transfer the files?

Does the .dms open with The Unarchiver?

Never heard of that, but good work! :)

Mail is not a good file transport. Sneaker-net via removable media works and preferably with HFS+ volumes and not FAT, but configuring a file share is usually preferable.