Each person continues to access their own storage using their own Apple ID in the same way as if not sharing. The only change is the billing and the amount of storage available. See the information in Share iCloud+ with your family - Apple Support including the following:
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.
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If a family member is already paying for their own iCloud+ plan, they can choose to switch to your plan or keep their own and still remain part of the family. When they switch to the shared family plan, they get a refund for the remainder of their personal plan. They can't keep their current plan and use the shared family plan at the same time.