One woman said that because of where she lives, in a coastal cellphone "black hole", she only heard about the text bomb eight hours later on Facebook.
Several people spoken with by the Northern Advocate said the important issue is not whether they were woken by a mistakenly sent alert, but that a message wouldn't reach them at any time.
Paulette Venables and her family, who live 50m from the beach at Otamure Bay, missed the early morning action. The household has no Vodafone or 2 Degrees coverage and can receive Spark "along the roadside a bit".
"And there is a place on the beach I can get reception if I know to go there, although that's not ideal if you're expecting a tsunami warning," Ms Venables said.
"[The text system] is not targeted at the people who need early warnings. How effective will a warning system be that doesn't have the ability to contact those who most need it?"
The Ministry of Civil Defence and Emergency Management (MCDEM) has apologised about what was meant to be a test going live during a trial of the system that will be available by the end of 2017.
The provider, based in Europe, trialled it during northern hemisphere daytime hours but it was meant to be restricted to a test circuit, not go to Vodafone customers all around New Zealand.
MCDEM director Sarah Stuart-Black said the texts were sent "in error".
"It is completely unacceptable and I take full responsibility and certainly apologise to every person that was woken by the messages."
But Steve Butel, who lives at Poroti, said a wake-up call is entirely appropriate for an emergency warning designed to save lives.
"I did wake up wondering what it was, and it woke me each time. I think it's a great idea and cannot understand why everyone is moaning," Mr Butel said.
"I think it was effective time-wise too as it's just as likely that a disaster hits in the middle of the night. This is about saving lives, so stop complaining."
Far North resident Allyson Waldron was also woken three times, and suggested maybe the authorities tested it in the day next time.
"We all know how important it is and that it needs to be done, just not at night next time, please, thank you."