According to ex-congregation members, families were pressured to give "love offerings" and other cash donations above the expected tithe.
However, the church has denied this and said none of its members were forced to tithe.
Mr and Mrs Tamaki have also defended their reputations in the past, following publicity around their lifestyle.
Last year, Mrs Tamaki - who owned several homes, drove a black Audi station wagon and had a $90,000 diamond ring, rejected claims she led an extravagant lifestyle.
"What is wealth? I don't have a lot of money in the bank but to me success is inspiring other people," she said.
Last month, it also emerged the church's tax-exempt status was under the microscope after it was issued with overdue notices for the late filing of annual returns for 14 Destiny-affiliated charities.
Six of these charities, which received a combined $5.5 million in donations in the most recent returns, are more than a year overdue in filing statements with the public charities register.
When contacted by the Herald about the photos Mr Tamaki tweeted, a spokeswoman for the church said the organisation had "no comment".
