"I was getting more and more upset and worrying about what was happening in Sydney ... I said my sister had been in an accident and I was trying to get to Sydney, but (the employee) wouldn't even acknowledge what I was saying.
"She just kept asking if I wanted to get on a later flight."
The passenger boarded a later flight.
In a statement to news.com.au, an airline spokeswoman said Tigerair would seek to contact the passenger if an internal review was "able to identify any system error on our end".
"We do sympathise with this customer's personal situation and understand the frustration of missing the check in closure time," the spokeswoman said.
"We are continuing to review the situation internally and we will certainly contact the passenger directly if we are able to identify any system error our end."
The spokeswoman said on-time performance was key to Tigerair Australia's philosophy, which is why the airline closed check-in desks strictly 45 minutes before flights "and we don't wait if people are late".
"On time performance is important to us, because it's important to our customers," the spokeswoman said.
"If you're late to check in for your flight or board our aircraft we can't wait, because it delays all the passengers who were on time and has a knock-on impact throughout the day. Our check-in desks close strictly 45 minutes before departure. We encourage customers aim to arrive 90 minutes before their flight to provide ample time to check-in and to allow for unforeseen delays on the journey to the airport.
"Tigerair customers can also web check in online up to 60 minutes before their domestic flight and head straight to the boarding gate 30 minutes before the flight if they only have carry on luggage. Checked in luggage does need to be checked in before the 45 minutes prior to departure check in closure.
"On the rare occasion that a customer does miss their flight, we offer a set fee of AU$85 to move to the next available flight."
Tigerair Australia offers travellers who arrive early or late to the airport to be transferred to another service on the same day for a small fee.
In May Tigerair achieved the unenviable ranking of Australia's worst airline in terms on complaints received.
In May, a pregnant mother claimed she had been forced to sleep in a bus shelter because Tigerair refused to let her fly.
The 34-week pregnant woman showed airport staff a doctor's certificate she said made it clear she was able to fly. On Facebook, the woman's husband vented his frustration against the budget carrier.
"I asked the Tiger staff if Tiger could give us an accommodation as my wife and child were both very exhausted and we had no money to book any last minute accommodation," he wrote.
"To which she responded 'your accommodation is not our problem we can only put you on another flight in the morning'.
"So here I am ... sleeping at a bus stop with my 34-week pregnant wife and a hungry two-year-old son."
The post was shared thousands of times.
Tigerair saw its complaint rate fall from 4.71 per 100,000 to 1.56 in regards to refunds, and from 2.28 to 1.48 in relation to flight delays or cancellations.
