Vizrt has been providing the graphics for the SD satellite LF since May 2011 and the HD satellite LF since September 2007. I doubt an actual STAR unit is in use for the satellite LF; it's probably an internal computer system with a custom Vizrt installation that is powering these graphics. If I had to take an educated guess, since November 2013 it's probably one system that powers both the satellite LF and the national feed LDL. It's not like the old days when you'd have a custom Weather STAR 4000 running the Travel Cities scroll.
As for when and how the current generation of the satellite LF is cued, it's very likely all automated, unlike the old WPS satellite LF days, when it appears that the satellite LF actually had to be manually cued. Back then, you'd see a relative amount of variation, maybe even a few second gap before the satellite LF would actually fade in. Now, it's a seamless transition from the Local On The 8s intro into the headlines section of the Satellite LF.