Yep, you will have to move the files to the new location. In terms of how to do it, even though you see a subfolder for the subdomain within your site's files, I never access it there. In my FTP client, I set up a new account just for the subdomain—so it's like setting up a separate account for any website. It has its own login details (although username and password may just be the same as for the main site.) You can see from this screen shot that it's mostly the same as for your main site, except for the Root URL and Remote Path:
Then, when you open that account in your FTP client, you are just looking at a regular root folder, just like with any other site, and you upload your files there.