I tried mounting storage using the new 'Bring your own storage' feature for app services on linux containers and there's some funky stuff happening.
For instance, I have a container running with basically a static site served by express in /home/site/wwwroot. When I mount storage in /home/site/wwwroot/assets/config, the entire /home/site/wwwroot folder is empty and the files that sit in the storage account do not appear in /home/site/wwwroot/assets/config (that folder is there though).
Apparently this was caused by the WEBSITES_ENABLE_APP_SERVICE_STORAGE being set to true. I figured this flag was required to enable the 'Bring your own storage' feature. Turns out this flag enables persistence of the container filesystem to Azure Storage in a different way as explained here.