Yes, the camera has to be attached to the computer via the USB cable while filming.
This might seem a little odd if you've been animating with a digital still camera, or an iPhone / iPod app. Animating the Stopmotion Explosion way is to use an animation program, which runs on your computer, coupled with a camera, which sends a video signal to the animation program.
Animation frames are captured and saved to the computer, either as video, or individual images. The program allows you to preview and save the animation as a movie file, which can be edited afterwards.
If you wish to animate on a mobile device, check out Stopmotion Explosion Animator for iOS!