The Government is using an automated system that cannot easily tell who lives overseas and who does not.
London-based IT worker, Laura, was among those getting a surprise payment, when she was technically ineligible.
She emigrated from Wellington eight years ago.
"I got an email on Saturday, the Saturday just passed. And it basically said, 'your cost of living payment will be in your account in two days' time'. Which was quite a surprise to me, because I didn't know anything about the scheme."
She will now opt out of future payments, she said.
IRD would not say how many people it had unintentionally paid overseas.
National's Nicola Willis said it was not just ex-pat New Zealanders but also former migrants who were affected.
She said National had heard from people paid offshore, including a man who left in 2014, French former visa holders and a man who left in 2019 and was now in the Philippines.
"My sense is this is very widespread, it's a major muck-up, it's like the Government pressed 'send all' - it's certainly not targeted and for ministers to be dismissive of it is I think quite disrespectful."
Prime Minister Jacinda Ardern told RNZ the vast majority of those getting the money were in New Zealand.
"But we have also moved quickly and so there will be some who are captured by the system, who aren't part of the criteria that's been designed but who may well receive it."
She said the Government was not "asking for IRD to actively go out and find those individuals, the cost of doing so would outweigh the benefit".
University of Canterbury business school professor Adrian Sawyer thought the Government would have been better prepared, to check if people lived offshore.
"The surprise I had is, I thought with their new computer system, that there would be mechanisms that would be reasonably straightforward to be able to verify."
Rhonda, who lost her job during the pandemic, told RNZ her life savings had halved since.
She had a disability and got the Winter Energy Payment - so she missed out on the cost of living distributions.
She said money given to overseas earners "rubs salt into the wound".
"That just stinks.
"It just feels really quite unfair. It's just another blow. It's not a huge amount of money, but it's just [saying], 'we're giving this to other people, even people overseas that are earning way too much, but we're not giving you anything'."
IRD said it would only try to recover payments if someone had provided fraudulent or wilfully misleading information.
In a statement, it said: "To determine whether a person is present and resident in New Zealand, Inland Revenue is using a variety of information including addresses, bank accounts and tax residency status. People must have had a 2022 tax assessment with eligible income such as salary and wages or bank interest."
It also said: "If someone has left the country and hasn't told Inland Revenue they're not living here currently, we will have treated them as resident here.
"Customers who weren't in paid work during the 2021/22 tax year could also receive the payment if they have income from bank interest.
"A student loan borrower's status is not a reliable way of determining if someone is in NZ or not, so this was not incorporated into determining eligibility."
People can return the money and opt out of the payments online on their IRD account or by calling 0800 473 777 if they have been wrongly paid.
