It often is a common feed. This is how the emergency alert system works, at least as I understand it - but note that I am no expert. I'll use an example of a weather alert.
Weather warning is issued by the National Weather Service. The alert goes out (with the EAS tones, which actually contain modulated data containing information about the type of alert, the geographical area, timing, etc.) via NOAA Weather Radio.
Your local radio station(s), TV station(s), and cable provider(s) have a device, such as a Sage EAS ENDEC, which is tuned to the weather radio station. When an alert goes out, if it's on the list of "important" alerts, this device will preempt programming - the broadcaster usually has no direct control over it - automatically to get the alert out there.
This is probably why you heard all of them at the same time.
There is also a situation where some broadcasters listen to other broadcasters. For example, in my area, we have a 50,000 watt AM station (it actually covers something like 37 states on good days). When a tornado warning is issued, first it's the weather radio, then it's said AM station, and then everyone else, because everyone else gets it from the AM station.
There's much more to it than that, but that's how I understand it. Hope that helps.