The five Spectrum staff with Covid-19 were in isolation, and their close contacts identified and asked to go into quarantine. Stowers said contact tracing in West Auckland had continued and found further positive cases.
He expressed frustration with the facility being named as a cluster.
"While we understand this is a fast-moving and fluid environment...it is also clear that reporting parameters, definitions and criteria must be consistent in order to maintain public confidence in the management process."
Identifying information about two clusters in Auckland had been withheld by the Ministry of Health but McElnay gave more details in a press briefing today.
Another cluster was linked to a "private party to celebrate an event", with 35 confirmed and probable cases. The event was held prior to the lockdown, McElnay confirmed.
"There is ongoing transmission happening from some of the people who were at the function ... that infection has passed within household bubbles during lockdown."
McElnay was unable to give more details, other than that the event was not linked to a workplace.
"What we are seeing with these private functions - and we see that particularly with the Bluff wedding function - is that social events, like weddings, like parties and other social events, really act as a mixing bowl for infection to be spread.
"We are seeing that in New Zealand and other parts of the world as well."
McElnay said not naming the Spectrum cluster until now, and keeping details of the private event cluster secret, hadn't compromised public health.
"While we haven't named them on the website, the work has been ongoing for all of those cases - every case that gets notified is followed up, and their contacts are followed up.
"It's only after you follow up each individual case, and follow up their contacts, that you begin to make the connection that they could be part of a cluster. And then there's a further investigation to try and find out where that source of exposure might have been. Sometimes it's obvious, sometimes it's less obvious."
After two staff at Spectrum Care returned positive tests last month, chief executive Sean Stowers told media that regional public health services had helped identify all people who had been supported by the employees, along with colleagues who had also been in close contact.
The staff worked in the Wellington and Auckland regions, and Spectrum's response was being guided by a special steering committee and crisis management team.