"She teaches me Portuguese and I teach her English," he said.
"This trip to New Zealand was to thank her for her assistance."
Vickers said he had informed INZ that he would be financially supporting Mendonca during her stay here.
"It is rubbish that she lacked money, I was waiting at the airport and not allowed to transfer money to her and her mother in Brazil was also not allowed to wire money into her account," he said.
Vickers was demanding an apology from INZ and was seeking legal advice about getting financial compensation.
Stephanie Greathead, INZ national manager border, said border officers identified Mendonca as a possible non-genuine visitor to New Zealand.
"Several factors led us to this decision, including the fact she did not have sufficient funds to support her stay, including no money on arrival into New Zealand, and discrepancies were identified during the interview between Ms Mendonca's and Mr Vickers' answers, regarding their relationship," Greathead said.
"Mr Vickers had also told border officers Ms Mendonca planned to study in New Zealand, meanwhile Ms Mendonca said she planned to return to Brazil to attend university."
Following an interview, Vickers was informed by a border manager the reasons she was refused entry.
After talking to Vickers, officers reviewed the interview notes and decided against overturning its decision.
While Mendonca was in the day room, Vickers claimed he received a message from her on Facebook claiming to be suicidal and sought the help of the police.
"Auckland Airport Police advised INZ they had received a message from Mr Vickers noting he was in Facebook communication with Ms Mendonca and she had told him she was suicidal," Greathead said.
"INZ immediately checked on Ms Mendonca's welfare and INZ staff called police in to assist."
With the help of a Portuguese interpreter on the phone, the agency said it discussed with Mendonca her current mental health.
"Ms Mendonca informed INZ that she was not suicidal, but was sad and wished to go home, she said she had never told Mr Vickers or anyone else at any time that she wished to harm herself," said Greathead.
"Regardless of this, police officers remained to monitor Ms Mendonca for the duration of her stay with INZ."
Greathead said there were certain conditions all temporary visitors to New Zealand must meet to be eligible for entry.
"The onus is on the visitor to satisfy INZ that they meet all of the entry requirements at the time they travel to New Zealand," she added.