So explain to me in layman's terms how something like this evolves. Do butterflies seek out mates with this particular pattern over time until it becomes the norm? If so, how do they recognize it in potential mates when only the caterpillar is capable of displaying it? If it's visible in the butterfly somehow, why doesn't it scare away mates like any other predator?
Or do the caterpillars just have chromatophores?
Evolution is blind. There is no deliberate choice being made. You have a population, an interbreeding gene pool that results in various traits developing. The resulting offspring live or die. Some are unhealthy and die, some are unlucky and die.
Natural selection consists of everything that impacts a population: what do the predators attack or avoid, what diseases are present, what is the climate like, what foods are available. All of these factors act as a sieve and the creatures with the collections of traits that give them the best chances of survival refine what genes dominate in the next generation's breeding population.
No caterpillar has to look like a snake to survive. But if it has some markings that scare off a predator, then it lives. If the breeding population's most successful survivors all have vaguely snake like markings those traits get passed on. the best snake mimics survive even better than the more vague snake mimics. The snake mimicry is refined with each generation until it's near dead on because it works the best. It will continue to work well for these caterpillars unless a snake eating specialist shows up in their environment. Then they're screwed.
Evolution is like a game of poker. There are multiple winning hands your genes can deal you. Whether you win or lose is dependent on what hands your competition are dealt.