How do they get the vitamin B12 into Marmite?

If you want to know the details of the process... sorry, I can't find that. I do note that the producers of Marmite list B12 as a separate ingredient, meaning they specifically add it as opposed to it being a normal part of the "yeast extract."

At a guess, it's produced by bacterial fermentation from some bacterial species that produces it naturally... something like Streptomyces griseus, Pseudomonas denitrificans, or Propioniibacterium shermanii. S. griseus was at one time thought to be a type of yeast, but it's now known that no animals nor plants, including yeast, are capable of making Vitamin B12. Only bacteria, which are neither animals nor plants (but are still considered "vegan" food sources), can do this.

Complicating this a bit is that some plants are capable of producing compounds that are similar enough to vitamin B12 that they actually test positive on the common B12 test, but these compounds are not biologically active... they're not "really" vitamin B12, they're just similar enough to fool the test.

Marmite adds supplemental B12 presumably because they realize this. B12 is produced by bacteria that live in the intestinal tract of animals, so there's B12 in meat, but vegans have a real hard time getting enough B12. They have an easy time getting B6, and that can help mask the B12 deficiency to some extent, but there's a significant risk of mental/neurological deficiencies if they don't get B12 from somewhere.