Image retention

When using centos:centos7 as a base image, and having saved a container started from it as a new image, does that newly save image still in any way link to the centos:centos7 image in such a way that if centos:centos7 is updated by the maintainer of that image, the newly saved image is auto-updated also? I assume not, but wanted to check.

A container is linked to its image - as its parent (the container layer only contains changes to the parent image)

however, you are correct, the container is not linked to the repo:tag alias, and will not be auto-updated when the image maintainer updates.