There isn't, except that you must have STORM WATCH toggled on in the app, as well as notifications on in the phone. I have both.
The NWS (National Weather Service), in cooperation with the Electric company, is what triggers Tesla's STORM WATCH mode. Tesla itself doesn't do it.
No, tesla triggers storm watch mode based on what you stated. Tesla triggers stormwatch due to alerts, not the other way around. I know this because there have been times when people have gotten alerts, and stormwatch still did not trigger. This is on tesla's side in relation to the alerts, not the other way around.