This summary is not the rule. The rule text controls.
Here's what this rule means for the people it affects.
If you were a special county judge in Broome, Chautauqua, Jefferson, Oneida, or Rockland County, or a judge on a children's court anywhere outside New York City, and you held that job at midnight on August 31, 1962, you automatically became a family court judge. You didn't need to run for a new election or go through a new appointment process.
You get to keep serving as a family court judge in your county for the rest of the term you originally signed up for. So if you were elected or appointed to a certain number of years on the bench, that time period still applies. The rule just changed your title and court, not how long you get to serve.
This rule was mainly about making a smooth switch when New York reorganized its court system in 1962. It let judges already doing this kind of work keep doing it, without any gap or disruption, as the courts changed from children's courts and special county courts into the new family court system.