I don't quite to figure out when a helm chart has to be pushed on a chartmuseum or any other repo.
I mean:
I hope I've explained so well.
In general, it is up to chart maintainers to push chart in any of that cases. More info about charts and verioning.
In your case, you will:
appVersion field in Chart.yaml file when the app image changesversion field in Chart.yaml file when chart resources are modified.Make sure you follow SemVer 2 standard when modifying any of those.