No, not all inward effects are consequences of outward administration. God is free to work outside of ordinary means.
However, that doesn't mean inward effects wrought outside of outward administration are themselves administrations. Administration is governance, a governing framework. Administrative frameworks are outward things, inherently. They are the "visible stuff", so to speak. As an example, the CEO and administrative officers, the vision documents, the conditions of employment are all administrative. Outward mechanisms intended to achieve particular inward ideals. The success of achieving inward ideals doesn't make that achievement a separate administration. It means the administration achieved the ideal.
In addition, the ideal achieved without an external framework means the ideal was achieved outside of administration, not that the ideal becomes the administration.