If they leave on the 30th they'll actually arrive on the 2nd, not the 1st (presuming travelling from the US)

The NZ govt website at https://www.govt.nz/browse/immigrati...a-or-an-nzeta/ states that you require an NZeTA if you are "arriving in NZ after 1 October 2019", which clearly arriving on the 2nd you would be. However the Immigration NZeTA site at https://www.immigration.govt.nz/new-...out-visa/nzeta states that "From 1 October 2019, you will not be allowed to travel to New Zealand if you do not have a visa or an NZeTA." which is far less clear in this case.

Timatic, which is what the airlines are going to use, hasn't been updated to include any specifics, and currently states "Effective from 1 October 2019, New Zealand will introduce the requirements, for some travelers, to have a New Zealand Electronic Travel Authority (NZeTA) and to pay an International Visitor Conservation and Tourism Levy (IVL). For more details, please visit https://www.immigration.govt.nz/nzeta"

Realistically I think the airline is going to be your problem. If you arrive at the border without an NZeTA and they decide you need one I can't see them turning you away - they are most likely going to simply waive you through, or worst case make you pay the IVL there and then. But if the airline decides you need one and can't board without it things could be a lot more complex.

There is a phone number on the immigration website you could try and see if they will give you an answer - but if it was me I'd be wanting to get that answer in writing to be able to show the airline at check-in if needed. If it was just the NZeTA fee I'd say just pay it as the few dollars is worth it, but the IVL increases the cost enough that it's probably worth finding the real answer...