Your web monetization status is active immediately. For the "Coil is paying" showing, users who are web monetized with Coil, have to install the Coil extension and that is what displays that.
Right now, I have a Coil subscription, that's why I have the plugin installed and that shows that web monetization is active. As a creator, you do not need to have a coil account ( except you want to add web monetization to your Youtube or Twitch channel). Users are the ones who needs to register and subscribe to web monetization on Coil.com .