This is the whole of Rocket Science. You can't test for some conditions, you can only test IN them by actually launching a rocket.
I think of it like diving into a pool. There is no way to practice diving into a pool before actually diving in. You learn to dive by diving.
If this is really the mechanism then I suppose tough to test (at least expensive to have large enough low-pressure test chamber to blow stuff up in), but it does seem odd they wouldn't just have explosive charges to destroy the rocket shell as well.
You can decide how long that is before and after, though I'll note that it may be complicated to determine what's not nominal: Starship has an unconventional staging maneuver that's basically a spin.
I'll also note that "they" didn't send anything; the FTS is autonomous, and will trigger on violation of its conditions, which is probably (1) departure of the instantaneous impact point (where the rocket will hit if all thrust stops now) from a safe ground corridor or (2) indications of disintegration of the vehicle. "The vehicle is doing something weird" is not a condition for flight termination.
The rocket tumbled for four complete revolutions. Most rockets will be destroyed by inertial and aerodynamic forces well before the first revolution (they are designed to withstand forces along the major axis, not significant side forces).
It was helpful from an aerodynamic force POV that the rocket was well over 100,000 feet before it started to tumble. Still, the inertial forces when the full stack started rotating must have been huge.
Ref: https://headedforspace.com/why-and-how-rocket-fuel-tanks-are...