Immortality, in it's pure sense, means that you can't die from disease, organ failure, cancer, etc. It doesn't neccissarily mean that the person with it cannot be killed, or that they do not age. Dracula is immortal, but he can be killed with a stake through the heart.
That's how the term is often used in fiction, but I consider it in incorrect definition, because if mortal means that you can die, then being immortal, i.e. not mortal, would mean that you can't, so a true immortal would simply not be able to die at all, a least not without exploiting some weakness, because fiction likes to give characters who would otherwise not be able to be killed weaknesses, probably because having your heroes never be in any danger would get boring, and if the invulnerable characters are villains, it would be pretty hard to stop them if there isn't some way to kill them, assuming that there is not a solution other than violence, and in any case, some examples of immortal characters who are unable to die due to natural causes or other things couldn't really be called invulnerable, as that would indicate not being harmed by physical violence, yet some characters who are considered immortal CAN be harmed by violence, it just doesn't kill them, at least not permanently, maybe they'll regenerate any injuries they recieve, or even if they're killed, they'll just come back. But that's just semantics that isn't really important here, basically, yes, the Nerevarine was not cured of corprus, as Vivayth Fyr tells you in the game, he only succeeded in removing the negative effects of the disease, things like the disfigurements, loss of the ability to reason, and such. But the positive effects still remain, in the game, the player becomes immune to all diseases after that point, and presumably the Nerevarine would also be unable to die from old age, but obviously, this isn't reflected in the game since you don't age during the game and it's unlikely that you'd play long enough to die from old age anyway. Obviously, the Nerevarine can still be killed by violent injuries, the game would be even easier than it already is if after that point in the main quest, you couldn't be killed at all no matter how much damage you took.
So in short, the Nerevarine still has corprus, but won't become a monster because of it, which works to fulfill part of the Nerevarine prophecy, which is probably why that part was important.