How does "disable and delete" work?

Ok, so I am going to give a quick background of what I have going on here. I keep getting pop up messages that my iCloud storage is full (not to worry, it is apple) and that I need to manage it. So I went in and saw that my messages took up a whopping 4.99 GB of the 5 GB allotted to us for free. I then went in and hit "Disable & Delete" and I got the standard warning that after 30 days, my messages would be deleted. I noticed something else, however, that has me a bit confused. It also says before you click that button that your device will automatically download the messages. Does that mean I do not actually have to worry about the messages being deleted or do I still have to do something to save them? If so, how?

Thanks!