How not to share my photos to other family member?

Photos are not shared unless you manually move them to a shared album.

That is true even if you are sharing iCloud Storage. See the following from Share an iCloud storage plan with your family - Apple Support

When you share a storage plan, your photos and documents stay private and everyone keeps using their own accounts with iCloud—just like when you have your own storage plan. You simply share the space available in the iCloud storage plan with your family members, so you only have one plan to manage.