You don't have to (and I assume most users don't), but you can if you want per-device reporting. You just set your router's DHCP server to hand out NextDNS's DNS servers.
ATT apparently removed overriding the DNS for IPv4 and IPv6. I had to double check because I thought I could do IPv4 but no.
There’s supposedly several options around it to use your own router but it’s not really worth setting up and my speed is slower using a second router.