The men scaled the tower just after 10am on Friday using a mesh rope.
Ms Burns said the first man to give himself up was checked over by medical staff and found to be fine.
"He's now having a meal, he's having a shower.''
One of his demands was to speak to a prison inspector and that has taken place, Ms Burns said.
Officials expected Forden to follow soon.
"He starting to indicate that he's had enough as well, of the elements, and he's hungry and tired,'' Ms Burns said this afternoon We will continue to negotiate with him and we anticipate that he will be down before too long.''
The men will be punished by being kept in their cells for 23 hours a day with restricted access for at least a fortnight.
"While this is not an escape attempt it is a breach to the good order and security of the prison.''
Despite their protest, Ms Burns said prison was "absolutely the right place'' for the men given the nature of their offending and subsequent behaviour.
The pair, who are believed to be housed in the prison's medium security wing, are unlikely to find sympathy from fellow inmates. The prison was under lockdown during the protest meaning no visitors were allowed over the weekend.
Forden has a long record of evading police and prison security.
He was on the run three times last year alone. Police starting looking for him in March after he breached bail. He was not caught for two months, during which he went on a crime spree.
In June he was to appear at the Whangarei District Court to face charges relating to his time on the run. Forden escaped from a secure room after an interview with his lawyer.
Police said he escaped by forcing a bar from the grille separating his area from the lawyers' room and was on the run for more than four months before being caught.
In October Forden became the first person to escape from the new $218 million Mt Eden Corrections Facility. He spent a week on the run before he was arrested.
He also escaped from Mt Eden Prison in 2008 by crawling through roof cavities to a tower and using a rope of knotted sheets to lower himself over barbed wire.
He was captured three days later.
By Abby Gillies and Sarah Thomas of APNZ