About 65 Kiwis have travelled from Sydney on to Melbourne since the arrangement began on Friday, with more expected to arrive on Monday.
Some have also arrived in Hobart, Adelaide and Perth, where they will be required to undergo 14 days of hotel quarantine.
Mr Andrews maintains the federal government did not inform him New Zealanders were entitled to travel beyond participating states and territories.
“People turned up without us knowing. People turned up without the WA government knowing. People turned up, I assume, without the Tasmanian government knowing,” Mr Andrews told reporters on Monday.
“These bubble arrangements were presented very clearly as just that – a bubble – and that if you wanted to be part of it, you could.
“We said no, we don’t think we should be at this time, however, it seems we are in it so we will make the best of it.”
Andrews has maintained the federal government failed to alert Victoria the New Zealanders were entitled to travel to other parts of the country after flying into Sydney or Darwin.
He said whether Victorians liked it or not, the state was now a part of the bubble.
“Let’s make the best of this and provide all the information that we can to people. That is the only option that we have got,” Mr Andrews told reporters on Monday.
He said more New Zealanders would likely be on board 17 flights from Sydney arriving on Monday, but they would not be required to quarantine.
“I’m not going to be quarantining people that came from a low-virus community and we just have to make the best of this,” Andrews said.
“If people turn up today on any one of those 17 flights, we will provide them with advice and support and we will make sure that they comply with all the rules as they relate to Victorians.”
Victoria recorded four new coronavirus cases and one death on Monday, bringing the state’s toll from the virus to 817 and the national figure to 905.
The Premier confirmed the latest victim was a male aged care resident in his 90s.
The four new cases, meanwhile, are all under investigation.
Queensland has recorded no new COVID-19 cases as health officials continue to urge people with symptoms to get tested after more virus traces were found in sewage.
Coronavirus fragments were last week found in wastewater samples from some Brisbane suburbs and parts of the Sunshine Coast.
Deputy Premier Steven Miles on Monday prompted Queenslanders with COVID-19 symptoms to get tested for the virus.
“Given we’ve had those positive wastewater results we’d really urge people in the southeast to go and get tested if they have any symptoms,” he told reporters.
Four virus cases remain active in the state with more than 1700 tests completed in the 24 hours to Monday morning.
Sewage samples taken at the Sandgate wastewater plant on October 12 and the Maroochydore and Wynnum wastewater plants on October 13 were found to contain traces of the virus.
NSW has recorded no new locally-acquired cases of COVID-19 and the government has flagged a further easing of restrictions in the lead up to Christmas.
There were just under 7000 tests conducted in the 24 hours to 8pm on Sunday, with four new cases detected in returned travellers in hotel quarantine.
It comes as Victorians woke to more freedom on Monday after COVID-19 restrictions were eased overnight.
Melburnians are now allowed to travel 25km from home and there will be no limit on time spent outdoors.
Outdoor gatherings have an increased limit from five people to 10 from two households, while facilities such as skate parks, golf courses and tennis courts will reopen.
Melburnians will also be able to get a haircut, see an allied health professional, renovate their home, wash their car and bid at an auction, though a number of strict safety protocols will be in place.
In regional Victoria, up to two people plus dependents are allowed to visit homes once a day, while hospitality venues can increase their capacity to 70 people outside and 40 people inside.
The regional city of Shepparton, which has been the centre of a COVID-19 outbreak, will not be able to host 40 people indoors for the time being.
The “ring of steel” that separates metropolitan Melbourne from regional Victoria will remain in place.
Melbourne will take another step on November 2, with hospitality venues able to seat 50 people outside and 20 people inside, while retail and beauty and personal care services can resume.
But Andrews indicated the next step could be brought forward, depending on Victorian case numbers in the next week.
He hit back at federal Treasurer Josh Frydenberg who called for restrictions to be lifted quicker.
“It’s all about the politics with this bloke, isn’t it? That’s all he does. He is not a leader, he is just a Liberal,” Andrews said.
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