While the citizenship is automatic, it is not automatically documented.
Minor children under 18 automatically become citizens when they are lawful permanent residents (green card holders) and live in the legal and physical custody of the naturalizing parent when the oath is taken. Parents must apply for a U.S. passport or file Form N-600 for a Certificate of Citizenship for their minor children to officialize their citizenship .
Adult children who are 18 or older when the nauralizaing parent’s oath is taken must file their own N-400 Applications.