I have a PoA that I would like to have notarized in NZ for use in Hong Kong. Do I need to have the PoA authenticated by the NZ DIA after it has been notarized?

It is always advisable to check with the authority or person receiving the document whether it requires further authentication after completion by the Notary. If they advise further authentication is required then the Notary can advise you on that or you can check the website (Authentications link) to determine what further form of authentication is required.
Hong Kong is an Apostille while the People’s Republic of China is a full authentication which then must be verified by the local embassy.