In "The Cask of Amontillado," there is a perverse pride that Montesor takes in his revenge and its methodology. In fact, the motivation for Montesor's narrative is to relate how cleverly he has effected his exact and appropriate revenge upon Fortunato. This first-person point of view is the lens of Montesor's irrational narrator whose main desire is to describe in minute detail his fulfillment of his family's motto: "Nemo me impune lacessit."
That Montesor tells his tale with the intention of instruction is apparent in his first paragraph as he states the lesson to be developed for his reader:
A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
Then, in his conclusion, Montesor displays a pride in the success of his plan, the development of his lesson, as he declares that
For the half of a century no mortal has disturbed them. In pace requiescat!
Thus, he has achieved his objective stated in the first paragraph.
Montresor does not tell everyone what he did to Fortunato. He very prudently refrains from telling anyone for fifty years, and then he is evidently only telling one person about the incident. I believe Poe intended to have his story understood as narrative written to a confidante in a letter. That letter would have been written in French or Italian, and most likely it would have been found among the friend's papers after that man's or woman's death. Then somehow or other it would have come into the hands of an American who was interested in old books and other old documents and curiosities, and that American, Poe, translated it into English and published it in an American magazine. It is also possible that Montresor wrote the confession in a letter one night while drunk and decided against mailing it when he became sober. In that case the manuscript would have been found among Montresor's papers after his death, and this could have been even more than fifty years after his commission of the murder. This, of course, is all part of Poe's fiction. It seems most likely that the fictitious Montresor would have written a narrative rather than telling the whole story aloud in a long monologue.