I suspect that although he turned rat, the family knew so many people growing up in Queens over the years that his daughters and extended family probably still kept in touch with a few friends on a limited basis...especially that his cooperation took place so many years ago.

And after he came back to NYC to that hospital/rehab center, was on his death bed, and then subsequently died, his family probably leaked it out in conversation to a few people. There was no longer any real danger to him because he already had one foot in the grave or had just died. The threat was gone at that point. It didn't matter anymore.

So thats probably how word eventually trickled down through the grapevine to local mob guys, who then spread the word around like wildfire.

Thats the most plausible theory I can think of.