Learn English – the meaning of “every of the sons”

Why does that construction exist?

Because in spoken language, should have and should of are indistinguishable (when enunciated as contracted should've). And some native speakers are so ignorant they don't understand that basic syntax requires an auxiliary verb after should, not a preposition.

But note that some perfectly competent Anglophones may deliberately write the incorrect version sometimes as a facetious usage. OP's cited Facebook poster probably isn't very competent, given that "next time" is future, so the auxiliary have (part of a "Present Perfect = Past" verb form) shouldn't be there anyway. But even people who know perfectly well that it's "incorrect" sometimes write things like a whole 'nother ballgame for much the same reason.

I don't know why OP wrote it's not correct to use should have. That's exactly what the Facebook writer should of¹ written!

¹ In case it's not obvious, that's me being facetious! But actually whereas one should've = should have done something in the past, when talking about a future "next time" it's what one should do (infinitive do, not have + Past Participle done).

Vladimir Harkonnen is dropping some words from the beginning of the phrase to make it sound more poetic.

What he's really saying, and would be understood is: "[You have followed] the bargain to the letter." Meaning that Yeuh has done exactly what was agreed upon when they made the initial bargain.