Good question. Last summer, the only skywarn net that I heard active was the one in Middlesex County (440 MHz Sayerville repeater). I dont remember the exact frequency on the top of my head. It did not activate for every single severe weather alert, but they activated it often.
Weather alerts these days are sent much faster via weather apps (Weather USA is the best one by far for immediate push alerts). I also subscribe to accu weather email alerts. If you live in Union County, their County Government website has a First Alert you can subscribe to for free. Of course you can also follow the NWS on Twitter and/or facebook.
But, my point is, HAM radio these days is no longer the best source for up to date weather alerts. With today's technology in satellite radars, the NWS is very good at passing on up to the minute weather alerts for any given location via certain weather apps, email alerts, and social media.