The new information, confirmed yesterday by the Ministry of Health, contradicts ministry information from the previous day that the person was part of the wider congregation and didn't need to isolate because they didn't have symptoms.
The visit also may have broken level 3 rules requiring people to stay within their household bubbles - but the Government is not looking to take enforcement action.
Auckland is currently at level '2.5', with the rest of New Zealand at level 2 - Cabinet will review the levels on Monday. Any confirmed changes to levels next week will take effect from 11.59pm on Wednesday.
But the chances of a move to level 1 next week look unlikely with health experts and epidemiologists saying they would like to see a consistent run of zero daily cases.
Under level 2.5, Aucklanders can travel outside the region but social gatherings are limited to a maximum of 10 people - apart from funerals, which can have 50 people.
The Mt Roskill Evangelical Fellowship Church is at the centre of the ongoing outbreak in Auckland, with all recent cases attributable to the bereavement sub-cluster - now with 24 cases and 101 close contacts.
Yesterday there were two new sub-cluster cases and two imported cases in managed isolation, bringing the total number of active cases to 120.
There are three people in hospital, including two in ICU.
The wider church group now has 45 cases, which is part of the whole Auckland cluster of 173 cases.
The Government has now moved to a multi-pronged approach to ensure ongoing co-operation from the church members and the sub-cluster.
That involves support from police, Māori and Pasifika health officials, community leaders, and Ministers Peeni Henare, Aupito William Sio and Jenny Salesa, as well as home visits and daily phone calls to ensure people are staying at home.
Health Minister Chris Hipkins said there now appeared to be good signs of co-operation, and as of yesterday morning 213 of the 332 people in the church congregation had already been re-tested.
The power under the Health Act to force people into quarantine remained an option, but Hipkins preferred not to use it.
"A punitive approach is likely to have the opposite effect to the one we want. We want people's co-operation. We don't want them to be scared away."
Previous non-compliance from the church group was based on a false belief that Covid-19 wasn't real, which Hipkins said had to be stamped out as much as the virus itself.
"What continues to be troubling and is threatening to block our path to level 1 is repeated, deliberate and malicious spreading of misinformation.
"We're continuing to see organised campaigns that are designed to confuse, and to sow doubt about our response."
He said the global death toll of 900,000 deaths was evidence enough of how serious Covid-19 was.
"This is very, very real. The virus is very, very deadly. There is no vaccine for it. The best protection we all have is through our collective efforts to give the virus nowhere to go."
The Ministry of Health said the visit on August 27 which sparked the sub-cluster underlined the importance of following the rules.
"As far as we can tell they were unaware they had been infected and were incubating and spreading the virus at the time.
"This underscores the importance of close contacts following the public health advice they're given, which includes strict self-isolation even if they don't have symptoms, and even if they have returned a negative test."
Disclosure of close contacts has also been an issue, with the St Dominic's student who tested positive being a contact of a previously undisclosed contact.
Whether that non-disclosure was deliberate was still unknown, Hipkins said.
He added that he hadn't heard "in any verifiable way" whether church members had taken part in an anti-lockdown protest.
He said more cases in the sub-cluster didn't mean there was no chance of moving to level 1 next week, especially if new cases were already in isolation.
The current settings - level 2.5 in Auckland and level 2 for the rest of the country - are due to expire at 11.59pm on September 16.
He didn't know how many close contacts or positive cases were yet to be identified when Auckland came out of level 3.
University of Canterbury mathematician and Covid-19 modeller Professor Michael Plank said those people posed a risk, but it was hard to quantify.
"Whether an infected person happened to take a bus, went to class with other students, or just went and did what people do on a day-to-day basis - all of that matters."
The concern was whether a super-spreader person went to a super-spreader event, like a crowded indoor school or workplace.