From that documentation I understand, that I need to place the customized config file dns-rebind-exemptions.conf directly inside the unbound configuration directory. So, unbound is installed at volume1/docker/unbound where the unbound.conf file and others are located. Therefore, I also placed dns-rebind-exemptions.conf in that directory, checked the config and restarted unbound.
Unfortunately, it's still not working. Do you think the problem is still the way, how customized config files are applied by the not-official unbound image?
By default, this image forwards queries Cloudflare DNS server over TLS. In other words, it does not act as a recursive server.
If you'd want a recursive resolver, you'd have to somehow replace the image's default configuration anyway. You could refer to Pi-hole's unbound configuration example and expand that by your private-domain line, but it likely would need additional tweaking to cater for running in a container.
If you are happy with unbound operating as a DoT forwarder rather than a recursive resolver, you may try to apply your changes to a file that is read by your mvance/unbound container.
It would seem that mvance/unbound's defaults are created by a script unbound.sh, and if I read that correctly, it only includes the following files: