You are right of course. There is still nginx taking care of everything. The point is that you need nothing but nginx/caddy/Apache.

Currently, I don't know any way how to initiate execution of scripts over http server so there is a systemd timer checking changes in files and recompiling the whole site. This has lot of downsides. The easiest would be if the static generator reacts on existence of a specific file - recompiles the site and removes the file afterwards.