Tantalum Capacitor Explodes When Engine Starts
Tantalums are very sensitive to overvoltage so you have to derate them if you want to use them. They are already typically derated by 30-50% in normal use but you are connect them up directly to a gas engine. Gasoline engines are a very harsh source of power so you should be installing transient suppression and the like anyways such as TVS diodes or MOVs to suppress voltage spikes. Regardless, you probably shouldn't have chosen tantalums in the first place as the input decoupling capacitors knowing they would be directly exposed to something so harsh as a generator.

No LDO, or any type of linear regulator that matter. Having a linear regulator defeats the purpose of having an the efficiency of an SMPS and they are too delicate for the protection task anyways. Furthermore, 18V to 12V with a linear regulator is too much heat for any remotely moderate levels of current.

Get a big TVS diode with a working voltage (not a breakdown voltage) as close to but greater than the battery voltage at full charge. It would help if you could scope to see what the startup transients, and the transients in general are like. There's a chance the TVS diode won't be able to handle the power in which case you need to go with a metal oxide varistor (MOV). But if a TVS diode can do it, then a TVS diode will be better. MOVs do not not clamp as well as TVS diodes and have an inherent wear out mechanism each time they conduct so you don't want to accidentally undersize it if you expect it to be constantly experiencing strikes or else it will wear out early, but they can be made a lot bigger (like bricks!) so can found in much higher power levels.

And go ahead and toss in that 50V aluminum polymer. You probably don't need quite so high as 50V though. Aluminum polymers don't need very much derating.

Might as well toss in a fuse while you're at it.