Remember the first war began over the question of who would take Messana, which Carthage had only recently acquired. Corsica they have had a lot longer. It was only after the whole first war, and the difficulties of the Mercenary war, that Carthage ceded Sardinia to Rome without a fight. But even then there was a great deal of resentment there and Carthage did try to take Sardinia back during the second war.