So just tried it out (don't ask how as wouldn't recommend). My phone had
the notifications blocked for some reason (Android), my wife (Iphone)
got the emergency notification from the Nest app (little underwhelming
notification ping but did work). I d...
Taking a look on Googles product details. There's two types of alarm
heads up and emergency. It says that only emergency alarms will trigger
a phone notification. Not tested but might be worth exploring