First, you have to have completed the last disaster before you start a new one, just like before the update. Once that's done, it's kind of like adding a specialization building: drag the "Meteor Strike" onto the Dr. Vu building and it will get sucked into that portal thing. Then an arm will come out and you'll see the part requirement for that disaster. Drag the parts into the arm just like you would for a building upgrade. Dr. Vu will hold out the big red button for you to press. Press it, and the disaster starts.
It's a few more steps than before.
