The Jekyll development server will rebuild on changes to files, but the docker run command in the Makefile does not bind-mount the _sass folder or any html files that are in the project root (such as index.html).
I tried mounting the _sass folder (-v "$(PWD)/_sass:/app/_sass") and it works as expected. However, I have been unsuccessful in getting the Jekyll server running in the Docker container to rebuild on changes when index.html is mounted (-v "$(PWD)/index.html:/app/index.html"). I found this SO thread that says you have to touch any individual files you want to mount in the Docker container before mounting them. I tried that, adding RUN touch index.html in the Dockerfile. It didn't work for me.
Others have tried the above and it works for them. Here's a Gist that includes a line to mount index.html. This code does not work on my system. Note that the additions in the Gist did not require adding touch index.html to the Dockerfile.