There is also a five-year waiting time for applications lodged before the change in policy.
Although the age of an applicant "freezes" at the time of lodgment, applicants with dependent children have been told their offspring will not be included if they go on to get married or find a high-paying job.
"An application must be determined in accordance with the immigration instructions in place at the time the application is lodged," said the general manager of visa services, Nicola Hogg.
"However, at the time the application is assessed, the dependent child must meet the other criteria such as being single, with no children of their own, and being totally or substantially reliant on the principal applicant and/or the principal applicant's partner for financial support."
Ms Hogg said demand for residence under the category exceeded the number of places, and one applicant had been waiting since 2005.
An Indian applicant with a 23-year-old son said it was ridiculous for the agency to demand that would be migrants "freeze their lives" for seven years.
"Some people go through the seven-year itch, but it is impossible for anyone to have a seven-year freeze," said the applicant, who did not want to be named fearing it could jeopardise his application.
His son would have turned 30 by the time he got his residency, and it would be "natural progression" for him to "get married and find the best possible job".
Family parent category queue
• Tier one (wealthy) applicants: 6 months
• Tier two applicants: 7 years
• Applications lodged under previous scheme: 5 years
• Allocated number of places: Up to 16,500
Source: Immigration New Zealand