Is it expected that specifying version 19.03.8 in my config.yml would actually install 19.03.9?
Depends, without seeing your config I can only guess.
My guess, you are looking at the wrong version. If you are using the Docker executor, docker --version only returns the version of the Docker CLI you are using. Which depends on the image you are using. This post is about remote Docker, which is the engine your Docker CLI connects to through a network. Each is a different piece with its own version.
You can see the full version details of both pieces by running docker version (notice no dashes). I hope that helps.