Northern Police Communications Centre Inspector Kerry Watson said there was major congestion on George Bolt Memorial Drive and the State Highway 20 connection.
He said many vehicles pulled over and parked on the side of the road in order to cheer the passing bus, with some supporters' fervour getting the better of them.
"We were getting reports of cars facing the wrong way on the motorway, and people running out in front of the Tongan bus," Mr Watson said.
"It was quite chaotic for a while."
At the airport, loud singing and the chanting of "Tonga, Tonga, Tonga" could be heard from the carpark - well away from where the welcome parade was going on outside the arrivals terminal.
A kapa haka group had to use a microphone to be heard over the crowd, who still drowned them out.
As the doors opened to reveal the 'Ikale Tahi team, the crowd roared, horns beeped and flags shot to the sky.
Auckland Mayor Len Brown said: "Let's welcome them to Auckland. It's red and white [but] it's not Nuku'alofa, it's Auckland."
Traffic light phasing had to be changed on the roads leading away from the airport in an effort to clear the backlog, while traffic coming towards the airport was also backed up towards Massey Rd.
Auckland Airport spokesman Richard Llewellyn said the barrier arms to the carpark were kept up after the official greeting in an attempt to get the traffic moving.
"After the Samoan welcome we were expecting a high degree of interest in this one," he said. "It was a fantastic welcome for the Tongan team, I don't think they could have asked for anything more than that."
Despite the heavy congestion, Mr Llewellyn said it didn't appear anybody arriving at the airport missed flights.
A convoy of 150 to 200 vehicles followed the bus to Greenwoods Corner in Epsom, where another 2000 fans were waiting at another welcoming event organised by the Tonga RWC Komiti 2011 supporters' group.
Mr Watson said the size of the convoy was unexpected, and at least 20 police officers were involved in trying to clear the resulting congestion.
"Initially [the congestion] was really, really bad to the point where road blocks had to be put in, in and around Pah and Manukau Rds, just to divert the traffic and keep it moving, otherwise it wasn't going to get through."
Mr Watson said the police would learn lessons from the day, but "we couldn't really anticipate what the supporters were going to do and that's where the problem lay."
Chairwoman of the Tongan supporters' group Rachel Afeaki-Taumoepeau said the Tongan team had been surprised by the welcome.
The community turnout was typical of Tongan nature, she said.
"We're very patriotic. Historically, Tonga is opening the tournament with New Zealand.
"It's a grand scale, so it gives us a chance to show how we support our team, the Pacific way."
Auckland Transport spokesman Wally Thomas said last night it was fantastic that people were getting into the spirit of the rugby tournament but "certainly over the top to be stopping traffic and dancing in the road".
Mr Thomas said he happened to be driving along Pah Rd, on his way to the airport, at about 1pm.
"It was very cool - there were kids getting red balloons and everything, and banners up on fences," he said.
"The spontaneity and excitement is fantastic but there has to be a level of common sense."
- additional reporting: Mathew Dearnaley
