I am afraid, you are confusing how volumes and containers work.
Each container created from an image will share the files backed in into the image layers of this particular image and have a copy on write layer on top to write data. If a container modifies data, it will be on its private cow layer. Though, this is not related to volumes.
Volumes are used to map an external ressource into the containers filesystem. The ressource itself will be managed outside the container.