He had introduced himself to one of his new neighbours and allegedly said he was recently in prison for a misunderstanding over sexual connection with a "very slightly underage" girl.
He said the courts should have let him off.
A resident then searched the trust's database search.
On July 17, police and Corrections staff visited the residents, and Jolly was moved to an Auckland address within 24 hours.
He had been paroled to Whangarei on July 12 after an acquaintance offered to put him up.
Neighbours refused to talk other than to say they had been upset to learn who their new neighbour was.
Jolly's Parole Act extended supervision order (ESO) was imposed for 13 years in the Hamilton District Court in April 2011.
One of his more recent breaches of his ESO conditions, in 2015 in Dunedin, involved the use of a smartphone. Police saw him using it for an hour in a Wi-Fi area.
He has also cut off his monitoring device and left the paroled address.
Sensible Sentencing Trust founder Garth McVicar described Jolly as "one of the worst we've had in this country".
"We've followed him around quite a bit. He's been moved around, he's shown up in Wellington, the Waikato, Dunedin."
During a sentencing hearing in Christchurch District Court on October 1, 2015, a Corrections report presented to Judge Gary MacAskill stated: "Given [Jolly's] over 30-year offending history, both sexual and dishonesty, he is considered to be at very high risk of reoffending and high risk of harm to potential victims.''
It is 12 years since his last conviction for sex offending and his existing ESO lasts until 2023.
Corrections acting northern region operations director Pauline Hopa said Jolly's status would continue to be monitored and options reviewed for ongoing management.
"Community safety is our top priority and we would not place an offender at an address if we considered that there was an undue risk to the community," Hopa said.
"We are tasked with returning offenders back into the community and want to make this work for everyone.
"This offender's conditions are comprehensive to ensure, as far as possible, the safety of the community."
She said the fact he had breached his conditions "a number of times and been held to account on each occasion showed the tight management by Community Corrections".
McVicar said ESOs were easily broken and the public's safety, rather than offenders' rights, should be paramount.
The trust has called for tougher restrictions such as already existing but never-used Permanent Public Safety orders.
It has also called for restricted, but not lock-up, living facilities for those offenders - possibly within prison grounds or other monitored sites.
