Most airlines allow you to manage bookings either online or by calling up their customer care numbers. Charges may apply for making changes but more often than not they are applied for changing flights rather than changing passenger details. (N.B. Changing the passenger who will fly is almost never allowed.)
Air Asia does have an online booking management option and states in its FAQ:
If you have booked using your old passport details which has now
expired, you can update your new passport details online via Manage My
Booking, contact our call centre for assistance, or visit our nearest
sales office/airport sales counter to update your booking.
Air New Zealand doesn't explicitly state whether changes to passport details are allowed but its FAQ does state:
However if you complete a booking and later find you have made a
genuine mistake, please Air New Zealand just as soon as you realise.
We'll do whatever we can to help.
You could always tell Air NZ that you accidentally entered expired passport details instead of the new one. This should be allowed as this is mostly a case of updating their passenger information system.
JetStar also allows changes to bookings online. I've flown with them and I do remember there being an option to update passenger details. However, I don't have a current booking with them so I can't confirm this for sure (but it probably is present).
It's advisable to make the change online or by calling up the airline in advance. Most don't make a big fuss of it and rather that than having to explain an employee at the checkin counter.
One more thing. This isn't related to this particular case but it's an important point so I think I should mention it. Flights to/from the US require passengers to update details on US Customs and Border Protection's Advance Passenger Information System (APIS) through their airlines, although requirements on who need to provide this varies. In this situation it certainly becomes important to update passport details in advance. However, I've found that even airlines which don't fly to the US or on flights that don't go the US ask for APIS details; possibly because they're plugging in the same server-side processing software and can't be bothered to customise it?