As he does with Fortunato, Montresor manipulates his servants in order to get his way, and avoid suspicion in the process.
Montresor premeditated his murder and knew that it would be best to have no witnesses; this is another factor influencing his choice to find and imprison Fortunato during the Carnival, when the abnormal amount of unusual activity would make his own go unnoticed. Montresor told his servants that he was leaving, and would not return until the morning. Then he told them not to leave the house for any reason. He knew that his servants, unable to resist the allure of a free night out, let alone one during the Carnival, would disobey his orders and every one of them would leave the house.
This serves as a double alibi; if suspicions were directed at him, not only can Montresor say that he was not in town at the time of Fortunato's disappearance, but none of the servants are likely to admit that they had disobeyed their orders, and would instead say that they were at home on that evening, and never saw Montresor nor Fortunato. This also fleshes out Montresor as a Machiavellian character who excels at using people's vices to get his way.
The answer to this question can be found soon after Montresor announces that he has an Amontillado for Fortunato to try. Montressor and Fortunato make their way to Montresor's house, and the house is completely deserted. Not a single servant is present.
Montresor provides a hilarious reason for why all of his servants are gone. Montresor told his servants that he would be gone all night, and none of them were allowed to leave.
There were no attendants at home; they had absconded to make merry in honour of the time. I had told them that I should not return until the morning, and had given them explicit orders not to stir from the house. These orders were sufficient, I well knew, to insure their immediate disappearance, one and all, as soon as my back was turned.
Of course the servants are going to leave. It's carnival, and that guarantees a riotous good time for the servants. Plus, the servants know they won't get caught, because Montresor told them he would be gone. It's like when your parents go away for the weekend and tell you not to have friends over. Of course you're going to have friends over.
Montresor's explanation for why the servants are not present is a very brief moment in the story, but it provides further evidence for how good Montresor is at using temptation to lure people into the action that he desires. He tempts his servants with a free night out, and that guarantees an empty house to commit the murder. He tempts Fortunato with a rare wine, and that guarantees that Fortunato will follow Montresor into the cellar.