After customizing a little my docker_compose.yml settings to include only ONE private server, I've noticed that upon restarting, all of my servers were suddenly private, using the same password.
However, in the docker_compose.yml file, environment parameter SV_PRIVATE was triple-checked to be set to 0.
After looking a little around, I've noticed that upon creating a server, a file named q3config_server.cfg was created which contains persistant settings that are loaded AFTER the config file.
To fix this issue, I've had to add this line at the beginning of servers/base/start.sh :
rm defrag/q3config_server.cfg