A number of police cars also followed the vehicle "to maintain observation of it", the IPCA decision said.
A second pursuit began as his driving worsened and it became clear that he was aware police were following him.
It ended when Eccleston stopped the car at the top of the Harbour Bridge.
He jumped over the railings and died from the injuries he received.
"Having multiple police vehicles continuing to follow Mr Eccleston, at speed, to maintain observation does not comply with police fleeing driver policy," said authority chairman Judge Colin Doherty.
"Although the officers involved stated that they were observing Mr Eccleston and were not in pursuit, the authority is of the view that their actions did amount to a pursuit.
"The authority's investigation found that Mr Eccleston's driving had not improved and the risks had not diminished.
"Therefore the second pursuit should not have been commenced in the circumstances."
The fact that police did not comply with the fleeing driver policy may have placed additional pressure on Eccleston - and potentially increased the risk of harm to police and other members of the public.
Auckland City district commander Karyn Malthus said police acknowledged correct policy had not been followed.
"Police were concerned that Alaric was heading back to his ex-partner's house and knowing that he had a violent history and was believed to be in possession of a firearm they wanted to do everything they could to safely apprehend him and keep his ex-partner safe," she said.
Every officer involved in the pursuit had the "best intentions and this was a very fluid and complex pursuit", Malthus said.
She noted that Eccleston was believed to be "unpredictable" and posed a risk to the community and specifically his ex-partner.
"This incident had a tragic outcome and we acknowledge that there were things we could have managed better in the pursuit."