Two TPS5430 inverting buck-boost converter modules failed in a row, am I using them wrong?
From the application note you linked to:

The output voltage is negative and is available at the device ground pin; so, the effective voltage across the input of the device is Vin –Vout. This difference must not exceed the input voltage rating of the device. Make sure not to tie the ground of the device or the exposed PowerPAD™ package to the system ground.

That is to say, the \$V_{in}\$ maximum rating applies to the difference between the input voltage and the output voltage.  That's about 24V for your inverter (12-(-12)).
The real sticking point would be the voltage across the built in switching FET.  It has the same limit as \$V_{in}\$, but is in a position where it may be exposed to higher voltages (ringing in the inductor.)
I think you have two options:

Use a lower input voltage (and hope that it doesn't blow.)
Find a better module.