They never notified archive.today of the illegal material, instead they chose to demand blocking actions of archive.today from a DNS provider. I would be interested to know whether any other DNS service providers have received similar such demands.
I would assume (like any normal individual), that you would notify the service first (archive.today) and if they've proven to be a non-responder to CSAM material then escalate to legal action.
If archive.today is honest about never receiving a prior notification, then the way in which they've decided to go about removing the illegal material is very suspicious.