They set it themselves on each channel manually. afaik, no manual or automated NSFW tagging by admins, only server owners.
From the link: "Owners of communities designated NSFW by Discord will have to submit an appeal if they wish to have the NSFW server-level designation removed."
That doesn't sound like self-designation is the only path to being marked NSFW.
The way I understood it, you can designate your server, but if the admins come across a server that should be NSFW, they will mark it. I imagine it comes from user reports of content.
Sounds like it will be punitive. You need to enable content filter (non negotiable) to enable community features. Content filter does not apply to NSFW channels. What will likely happen is that if content filter keeps "detecting" NSFW content in your channels in which it operates (non-NSFW channels) it will eventually tag the whole server as NSFW.