I want people to have to register before they can upload files to the Downloads app. 

I've checked the permissions and downloads settings on 'guests' and I have the permissions set so they can't upload but when I've tested it they can still upload and it says they can make an account later

'You can post now and register later. If you have an account, sign in now to post with your account.'

Anyone know how to fix this please? 

That’s because you have Post Before Registering enabled so it checks the Member group permission. 

Where do I turn this off?

Type Post Before Registering in the ACP Live search and click in the results to disable.