Sharing iCloud storage to family member with existing storage plan

That is correct except for "family members storage content automatically moved to the shared family plan" -- their content stays where it is under their Apple ID; it is just a change in how the billing is handled.

Also see the following from: Share an iCloud storage plan with your family - Apple Support

If a family member is already paying for their own iCloud storage 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.