First Union, which represents 4000 bankers, has had an influx of calls about the pressures bank staff are under to meet sales and customer service targets.
This comes as ANZ confirmed it sacked seven staff who deleted customer email addresses last year to prevent them from giving negative feedback.
First Union represents frontline bank employees, including 900 ANZ staff, and general secretary Dennis Maga said the bonus culture was to blame for the staff's desperate attempt to avoid negative customer feedback.
"What ANZ must do now is reflect after this incident because this is also a byproduct of their scheme that they introduced to their staff to the point that they became so desperate. It's not acceptable but it's happening," he said.
ANZ said yesterday it took customer feedback seriously, and seven staff involved lost their jobs for this and other disciplinary matters.
ANZ has been in the spotlight recently, first for miscalculating the amount of capital it's required to hold and second for the departure of its chief executive David Hisco in an expenses dispute.
Last month, the country's main retail banks promised to largely scrap sales incentives for frontline staff and their managers.
The incentives, which emerged from last year's inquiry into bank behaviour, pointed to customers being pressured to buy financial products as frontline staff tried to meet sales targets and earn commissions.
Since the announcement, Mr Maga said the union had received several complaints from its members concerned about the bonus culture.
"It's actually the number one complaint from our members about the sales targets. Now that the FMA has released that report, staff are starting to come out and say publicly or even anonymously the way they've been pressured during those days."
The Financial Markets Authority's report into the country's bank culture and conduct, released last November, shows it was aware of the bonus culture - although no banks were named directly.
The report included an instance in which staff at one bank manipulated records to prevent customers from receiving satisfaction surveys.
This happened if it was likely the customers would provide negative feedback, which in turn could lead to staff losing incentive payments.
Former BNZ chair Kerry McDonald said it should have been a clear warning about banks' internal work culture and - in ANZ's case - firing the staff was not the right way to deal with it.
"It is a real warning sign if staff are too scared to engage in a process because they fear retribution," Mr McDonald said.
"It suggests there is a lack of trust amongst the staff because if they're too scared to undertake a customer survey they're obviously scared of the response but in a well performing, well-run business, that issue wouldn't occur."
Mr McDonald said the country's banking sector needed much more intense scrutiny than it was getting.
"It's also a sign of the weakness of the FMA that they didn't do anything about it. They're meant to be a regulator, something like that is a serious warning signal but they simply noted it and didn't respond."
In a statement, the FMA said the intention of its review was to highlight themes rather than individual practices.
"Our statement on bank incentives last week acknowledged that banks had committed to removing sales-based incentives for frontline staff and that the real test of the success of these commitments will be the type of behaviour that is rewarded in the future."
