Sub-transaction privacy means each party sees only the transaction parts it is entitled to see. Every action has informees, the parties that should learn about it. Under the projection rule, an informee sees that action and its consequences, but nothing else. For a create, informees are signatories and observers. For a consuming exercise, they include the consumed contract's stakeholders, the actors and any choice observers.
An atomic transaction commits every action or none. In delivery versus payment, Alice pays bank-issued cash while Bob delivers a bond recorded by a registrar. Both traders see the whole trade. The cash bank sees only cash, the registrar only bonds, and outsiders nothing. A failed bond leg means no cash moves. Privacy has limits: synchronizers see metadata, mediators see informee lists and confirmation results, and divulgence can reveal contracts to non-stakeholders.