In a press conference today, Andrews said Victoria authorities had been alerted to the increased number of breaches by Australia's federal government.
There were tearful reunions at Sydney International Airport as the first flight of the new trans-Tasman bubble arrived from New Zealand.
But the Victorian government has said it did not expect to receive global travellers as a result of New South Wales making a travel bubble arrangement with New Zealand.
Victorian officials had reportedly asked the Australian Border Force to speed up the release of passenger lists to prevent a repeat of the surprise arrival when more flights land from New Zealand, it said.
"My advice to Minister Tudge is instead of stubbornly defending this, work with us, and let's make sure Victoria is not part of a bubble we never agreed to be in", he said.
Andrews said his state had now effectively been forced into accepting the arrangement.
"We would prefer better management of these arrangements but this is something that happened that was outside of our control", Western Australia Premier Mark McGowan said on Sunday.
"Their own chief medical officer was at the meetings where this was discussed".
Professor Sutton today clarified he was not present at the AHPPC meeting in the moments when the New Zealand travel bubble was discussed, even though he did attend part of the meeting.
The Australian state of Victoria reported four new Covid-19 cases on Monday (Oct 19) as people in Melbourne were granted more freedom to move about after a months-long lockdown, buoying hopes an outbreak in the city was nearing an end.
It is the sixth consecutive day cases have been in the single digits, and the fourth in a row they have been below five.
Deputy federal opposition leader Richard Marles, appearing on ABC News on Monday, also said it should have been the responsibility of Australian Border Force (ABF) officers to restrict the incoming worldwide travellers to participating jurisdictions. "They've got a responsibility in this respect and they should be taking it", he said.
"It beggars belief that once again, the Federal Government seeks to avoid responsibility in this manner".
However, he conceded the state was now apart of the travel bubble, with the state's website detailing New Zealanders are free to enter without requiring to quarantine.
Another 23 of the bubble travellers flew onto Perth, which does have restrictions on visitors from other Australian states, so the 22 adults involved are in hotel isolation in Perth, and one child is with a family member in Perth. If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.