One answer: the files are stored in git and the image is built on commit and tagged with the current ref, then pushed. The deployment is then updated to reference the new tag and services are restarted, pulling the new image and launching the new container. This is the typical ci/cd setup for kubernetes deployments.
How are changes getting put into the container? Are you versioning the container each time a file is changed or added? When files change are all instances of the containers being restarted to get the new/changed files?