Since no one is responding, I am giving it a shot.
I don't know whether this message means that a new image is pushed for either a new or an existing tag.
Back then, when I was still using Pihole, I know that they add environment variables to their images, that are image specific, and end up in the created container.
If you pull the updated image with the Container Manager, and reset the container, the old container configuration will be applied to the new container. Watchtower and Portainer will do the same. This behavior usually works great with most images, but can cause problems with the Pihole image (I remember that it did a couple of times in the past).
Though, if you use docker compose for updates, there won't be a problem, as it will always remove the old container and create a new container using the configuration you configured in the compose file.
The question is: what are you using to manage your containers?