For a integration repository to be valid these are the criterias:
The repository uses GitHub releases (Optional)
If there is releases:
When installing/upgrading it will scan the content in the latest release.
If there is no releases:
Update will not be possible (but the user will still be able to install/reinstall it).
It will scan files in the branch marked as default.
There is only one integration (one directory under >ROOT_OF_THE_REPO/custom_components/) pr repository (if you have more, only the first >one will be managed.)
The integration (all the python files for it) are located under >ROOT_OF_THE_REPO/custom_components/INTEGRATION_NAME/
In that integration directory, there is a manifest.json file.
Looks like custom_updater is moving on to HACS. Repository would need to change the directory structure a little to make it work:
https://custom-components.github.io/hacs/#add-custom-repos