Poe gives the story a timelessness, both an antiquated and a modern feel to it. The use of the Italian (Roman) Carnival setting where the ancient Christians are buried in the catacombs is marked by time and Gothic motifs (the masked party-goers are dancing on the graves of martyrs).
The name "Fortunato" is marked by time: "fortune," as you know, deals with the chance, luck, fate (that which cannot be controlled by time). Also, the Amontillado (which doesn't exist) is valuable only because of time (its vintage, its age). The story is set up as a frame, with 50 years passing between its telling and action: it has had time to become vintage as well.
"Time" is mentioned 3 times in the story:
Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity--to practice imposture upon the British and Austrian millionaires.
There were no attendants at home; they had absconded to make merry in honor of the time.
I paused again, and this time I made bold to seize Fortunato by an arm above the elbow.
The time refers to both the act of revenge and the Carnival (Mardi Gras) atmosphere. Poe uses the paradox of time cleverly in the story: using a time of joy and revelry to divulge a murderous revenge plot.
The ending of the story gives the reader the most important marker of time:
I hastened to make an end of my labor. I forced the last stone into its position; I plastered it up. Against the new masonry I reërected the old rampart of bones. For the half of a century no mortal has disturbed them.
In pace requiescat.
Notice, he uses the paradoxical language of both "hastened" and "half a century." In other words, Montressor cannot wait to kill Fortunato, but he can wait 50 years to tell us the story. The use of Latin is the perfect touch at the end. It is like a gravestone marking Fortunato's grave.
The irony, of course, is that no contemporary of Montressor is likely alive (he would be 70 or 80 years old) during telling of the story to verify the accuracy of it. Also, there is no evidence linking Monressor to the murder, since 50 years is time enough to rot a corpse. One wonders if the crime took place at all? It could be the tale of a madman with only a revenge fantasy. The point is, I think, that imagination cannot be controlled by time (the past, present, and future co-exist in the mind simultaneously).