will those sharing the plan be private

See the following from Share iCloud+ with your family - Apple Support

When you share an iCloud+ subscription, everyone in the family group uses their own account. That way your photos, documents, and other information stay private, even though you're sharing access to the service. You simply share the features and space available in iCloud+ with your family members, so you only have one plan to manage.

All their information will stay private except for their purchases, which are shared with family members.