You maybe misunderstand the drupal configuration workflow. A modules config files will only be installed when installing the module. At that moment the configuration will be imported in the database, and so, when you export the sites configuration your modules config will also be part of that. Subsequent changes to configuration of your own module can be done in update_hooks, but it's easier to make changes on the site self, export that, and have it versioned in that site's repo. If your module only holds config, you could also uninstall it immediately after you installed it, because it doesn't serve a purpose anymore.
So doing this, exporting config to a module, makes sense when you need that same configuration on another site that doesn't already have that configuration. Its a quick way to setup parts of the site the way you like. If a customer wants events where users can register to, and you created that before, you could create a module for that, that when enabled on the site sets up the basics for it. Further customizations to the clients wish on that particular configuration will be versioned in its own repo, when exporting the sites configuration.