I just got my Tempest all set up and connected (even to Underground). There is a thunderstorm nearby, and even though I don’t have the mobile app (explicitly) running on any iOS device, mu Apple Watch is reporting the lightning strikes.
This is actually very cool, but I cannot find out how it is receiving the notifications. When the strike is reported, I see the icon for the Tempest app on my Apple Watch, but again, there does not seem to be an app on it, nor any other apps running even in the background.
Follow-up: Ok, I was also confused I only got 4 notifications from the watch, but have since discovered (on the forums) that there is an algorithm to stop notifications once the strikes become more frequent that a certain rate.