He was driven to fury by Tickell's publication, which had the appearance of a competition.

But angry as he was, he could find no real cause of complaint, except by imagining a fictitious conspiracy; and this complaint was never publicly uttered till long after Addison's death.

Addison knew, no doubt, of Pope's wrath, but probably cared little for it, except to keep himself clear of so dangerous a companion.
He seems to have remained on terms of civility with his antagonist, and no one would have been more surprised than he to hear of the quarrel, upon which so much controversy has been expended.
The whole affair, so far as Addison's character is concerned, thus appears to be a gigantic mare's nest.

There is no proof, or even the slightest presumption, that Addison or Addison's friends ever injured Pope, though it is clear that they did not love him.

It would have been marvellous if they had.