Mr Stoneley said that after discussing his case with a supervisor and then making calls, the Customs officer told him he could go.
He said he found this bizarre. He had been checked for Ebola when he flew out of Monrovia on a Kenya Airways flight at 6am on Sunday.
"I said 'The very least you guys should be doing is getting a thermal check to see if I have a fever. If I have a fever then put me in quarantine'," Mr Stoneley said.
"They said, 'Well we don't have any on site and I don't know where we could find one."'
Mr Stoneley said Customs photocopied his arrival card so they knew his address and told him they "would look into" getting a thermal scanner.
A Customs official confirmed the arrival of passengers coming from West Africa into Auckland on Tuesday and said they were questioned by Customs officers.
The official said the passengers stated that they were not feeling unwell, and officers observed that they were not displaying any symptoms of illness.
"They were therefore cleared to proceed and should have been provided with information on how to seek help should they subsequently become unwell."
The official said it is not Customs' job to do any formal testing. "Customs does not carry out health assessments or testing. This is done by Public Health officials who have access to the necessary equipment."
Mr Stoneley had been living in Monrovia since April, where he is working for a gold dredging company.
Figures released by the Ministry of Foreign Affairs and Trade show that in the past week, three other Kiwis have left Nigeria and one has left Sierra Leone.
A spokeswoman said it is providing consular assistance to one New Zealander still stuck in an Ebola-affected country. The person did not have Ebola. There were yesterday still 44 New Zealanders in the "four principally affected countries" - two in Liberia, six in Sierra Leone, 35 in Nigeria and one in Guinea.