"We were told to wait for approximately half an hour and then the lady came back to us with letters and said you have been volunteered to give up your seats due to overbooking with letters we had to sign.
"Then she gave us $350 each with a couple coffee vouchers and told us to come back tomorrow."
They boarded a flight at the same time the following morning, but Chandler said he was annoyed to miss out on a day of his much-anticipated holiday and the money offered didn't make up for that.
"Part of the reason I flew Air New Zealand was I thought we would get looked after better than this.
"I believe it's common practice for airlines to overbook flights in the hope some people won't show up but it just doesn't seem right that they are allowed to do that," he said.
"Our travel agent in Otorohanga told us they were selling tickets to our flight right up until a couple days before the 31st."
Chandler believed he and his family had been chosen to be bumped because they had bought the package on special.
An Air New Zealand spokeswoman confirmed the value of the fare paid was taken into consideration when bumping passengers from overbooked flights.
The airline apologised for having to "unfortunately" bump the party from flight NZ46 to Rarotonga, she said.
"Each of the four customers in this party received a $350 voucher as compensation and travelled to Rarotonga on the next available flight the following day."
Air New Zealand took a "highly conservative" approach in its booking system, she said.
"Our policy is to first ask for volunteers. If there are no volunteers, then staff make a selection taking into account a number of factors, including the value of the fare paid, any requests for assistance associated with a booking and Airpoints loyalty tier status.
Overbooking flights is legal in New Zealand, but the rules governing it are clear, including reasonable compensation for passengers.
Compensation applies to any reasonably foreseeable extra costs incurred as a result of the delay, such as meals, taxi fares, missed events and missed flight connections.