Commenting on an Instagram shot of Ross and Jayne where he tells her "204 countries + 7 seas and I had the privilege of meeting you", Collins said: "204 countries - maybe doesn't need taxpayer support."
Twyford said Collins' tweet was "essentially inciting victimisation of a young couple who just bought their first home".
"They didn't sign up for that. They feel bullied because of Judith Collins' actions."
But Collins said she was merely making a point about KiwiBuild eligibility, and turned the blame back on Twyford for any hurtful comments about the couple.
"He is the person who put this young couple up as poster children for KiwiBuild homes. There are plenty of other people he could have targeted and used.
"Other people have gone on about their personal circumstances. Certainly not me."
Collins denied that she targeted the couple in making her point about KiwiBuild eligibility.
"We've got a nice young couple, wanting to get ahead, put their names in for the lottery, lucky enough to get it, and all of a sudden people are saying, 'Well, hang on, we thought this was going to people in need.'
"I say good on them. But I also say it's $2b of taxpayer funding that is clearly not targeted at people who can't get on the property market."
Twyford was incredulous at Collins blaming him.
"She posted material that was on their personal Instagram page and incited right-wing trolls to victimise this couple, who committed the sin of buying their first home. She's got to take responsibility for her own behaviour.
"This woman's got no boundaries when it comes to anti-social behaviour online."
He said KiwiBuild wasn't just for the poor, but was about building affordable homes.
"There's a whole generation of young New Zealanders out there, many of whom are in good jobs, earning good money, and they cannot buy their own home in places like Auckland.
"Two teachers in Auckland who could take home $160,000 a year before tax, they are effectively locked out of the market because the gap between house prices and incomes was allowed to get so out of control.
"That's why we've set the income threshold at $180,000 [a year] for a couple in Auckland and Queenstown."
He said the Government had a broader programme, including building thousands of state houses, to tackle housing problems in New Zealand.