In many cases there is some opportunity to validate information before it goes out. In others ... not so much.
Even a missile-launch alarm would typically have some opportunity to be assessed based on alert values (e.g., increasing or decreasing hostilities), and perhaps multiple sensor systems (boost-phase IR tracks plus radar signatures, known planned non-military launches, etc.).
In the case of earthquakes, their very unpredictability, the brief period of time avialable in which to make an alert (often only a few seconds, in cases a few minutes) means that manual cross-validation is all but impossible. Still, checks across multiple seismic detectors, preferably isolated from one another to the maximum extent possible, would be one potential check, though you'd still need to have multiple sensors relatively close together, as the time of propagation of seismic waves is both what provides the early alert and causes the damage. (Relative speeds of P (primary) and S (secondary) waves helps --- the p waves tend to cause less damage, but provide an earlier alert, the s waves arrive more slowly but do most of the damage.
At the surface, speed differential is about 3 km/s, meaning there's roughly 1 second of arrival differential for each 3km the observer is from the epicentre. (Subsurface waves travel faster.) Each 3km of separation of seismic stations costs 1 second of advanced warning time, plus whatever system logic and response times exist.
But given that major earthquakes can occur suddenly and without warning or pre-shocks, you really do pretty much have to be ready for anything at any time. And alerting systems need to take this into account. One option might be to have the logic on the phone itself --- it would trigger an alert, but only if some number of independent alarms were detected. One would be unlikely to trigger a false alarm, but two or three near-simultaneous alerts would indicate a major quake.
Penalising false alarms is probably the wrong approach. An engineering philosophy, of determining paths to either false positives or false negatives (each of which have high impact), and eliminating those.