"We will...discuss the movement of our citizens between Australia and New Zealand," Mr Turnbull said in a statement on his visit, which also referenced the recent Anzac centenary.
Ms Airey spoke to the Weekend Herald a short time before Parakuka was transported to Yongah Hill detention centre near Perth late on Wednesday.
"The air con is on 24/7, the lights are on 24/7, he is not allowed to make any calls out...he is lost, he doesn't sound like himself at all...he hasn't been eating. The no sleep is probably what is making him delirious."
Parakuka, 35, came to Australia 18 years ago, and has two Australian-born children - 13 and 16 - from a previous relationship. The only family he has any relationship with live in Australia.
Ms Airey said he was informed on September 1 that his visa was cancelled because of a previous conviction of assault occasioning bodily harm whilst armed and in company, for which he served 18 months' prison time and received a suspended sentence.
She was now worried he would be sent to isolated Christmas Island, where 40 New Zealanders are held. About 200 Kiwis are in detention centres across Australia.
A spokesman for Australia's Department of Immigration and Border Protection said it could keep high-risk detainees within watch house facilities, "until such a time as they can be accommodated safely and securely within the detention network".
"If a detainee has a history of violence and has served a term of imprisonment, then it may be deemed as appropriate to accommodate these individuals in secure facilities, which at times includes gaols and watch houses."
The department did not address questions about conditions at the police watch house, or confirm why Mr Parakuka's visa was cancelled.
Marama Fox, Maori Party co-leader, said Mr Key needed to not "pussyfoot around" next week, and make clear to Mr Turnbull that such treatment of New Zealand citizens - whether they deserved to be deported or not - was appalling.