They came there to retrieve Cyclops in order to bring him back to the New York for the reading of Professor X's will. Not knowing what to expect Cyclops decided to go, but with the rest of his team in tow, including Kitty while the students stayed at their school. They were then whisked away by Magik's teleportation powers.
Kitty was present along with her teammates at the Jean Grey School when She-Hulk read the will and revealed to major secrets, that Xavier was married to Mystique and learning of the existence of Matthew Malloy. She stayed at the school while Cyclops and Wolverine assembled a small team to intercept Matthew.
Shadowcat witnessed the death of Cyclops and Magik through a telepathic shockwave created by the new mutant after they got caught in the crossfire between S.H.I.E.L.D. and Malloy. But Matthew was able to resurrect himself and teleported to the Jean Grey School, were she saw him obliterate Emma's diamond form with no struggle.