He did, from a certain point of view.
Dying and joining the wormhole aliens in an eternal, non-linear existence can both be viewed as the same thing. He is "dead" in that he is no longer living a mortal life. It's the sci-fi way of saying "he died and moved on to the afterlife."
Suddenly finding himself in the Celestial Temple, Sisko is told by Sarah that the Pah Wraiths have been returned to the Fire Caves and will never emerge again. His task is complete, and it is time for him to rest with the Prophets. The DS9 crew is puzzled by Sisko's disappearance until he comes to Kasidy in a vision, telling her that he has moved on to a new stage of his life. He assures her he will return, but because of his nonlinear nature, it could be in a year, or yesterday.
As some have pointed out in comments, The episode mentioned in the question, The Visitor, is just a self-contained plot that is resolved in that same episode. The possible future in which and elderly Jake says Sisko died is avoided when Sisko dodges the energy discharge that created the loop in the first place.
Ben suddenly finds himself back in the Defiant engine room, just after he saved the ship. This time he's able to dodge the energy discharge from the warp core. Jake is puzzled how his dad knew to get out of the way, but Ben, having seen how much his son was willing to give up in order to save him, can only hug him knowing they now both have a second chance.