Although the short story "The Cask of Amontillado" is not typically thought of as being humorous, it certainly has moments of dark humor. This issue concerning the masons is one of them.
When Fortunado makes the "grotesque" movement that Mostresor does not comprehend, he was showing the sign of "the brotherhood" of the Free Masons, an old secret society. So the irony is that Fortunado is referring to the secret society and Montresor pulls out "a trowel" showing that he too is a mason. The mason that Montresor refers to is the straight definition of someone who builds and works with masonry.
In the story the word "mason" is utilized in two different ways creating a kind of irony. The first is to refer to a member of an organization. The second is to refer to an individual who is a craftsman who works with stone.
The following conversation is from the portion of the story where Fortunado reveals that he is a mason in regards to the first definition.
"I looked at him in surprise. He repeated the movement --a grotesque one.
"You do not comprehend?" he said.
"Not I," I replied.
"Then you are not of the brotherhood."
"You are not of the masons."
"Yes, yes," I said; "yes, yes."
"You? Impossible! A mason?"
"A mason," I replied.
"A sign," he said, "a sign."
"It is this," I answered, producing from beneath the folds of my roquelaire a trowel.
"You jest," he exclaimed, recoiling a few paces. "But let us proceed to the Amontillado."'
So the answer to your question would be yes. Fortunado is a mason in the sense that he is a member of some kind of exclusive organization.
The narrator, who harbors some kind of unexplained resentment for Fortunado, mocks this status by sealing Fortunado within the catacombs as the second kind of mason creating irony withing the text.