I did a travel reservation with Amex recently over the phone (complimentary flight). I got the Amex itinerary immediately while on the phone and was told that I should receive the firm booking on or around 6 PM that day (given I was calling at 5 PM), which I did. You won't get an eticket from Air NZ but should certainly be seeing it showing in your Airpoints account when logged in or have received a ticket from Amex by now. I would be calling them.