The term 'phantom shift' generally refers to consciously drawing out the bodily sensations related to whatever animal/being you feel an association with. This particular article, as compressed and simplistic as it is, is in effect about phantom shifting.
As a note, medical Phantom limb syndrome happens after any form of amputation, involving nearly any body part. The brain has a map of the body and nerves, as a function of motor control and bodily awareness. This is why you know not only if you are being touched (or hurt) by something you also know -where- you are receiving that signal. This is also what allows your brain to do things like open and close individual fingers, turn your wrists, rotate your ankles, or any other manner of motor function. Making a fist involves the brain firing a pattern of neurons which connects to a line of nerves down the arm to a specific set of muscles so they contract while others relax. Even if a person has no hand to clench, the rest of the nerves from brain to amputation point still exist. The brain expects the hand to still be there, and continues to operate as if it still is. This includes expecting to be receiving signals and feedback as well. Like touch, temperature, pressure, etc. So the brain thinks the hand should be a fist, clenched, cold outside and warm palm, pressure from squeezing fingers, muscles giving feedback of tension, changing blood pressure, and a host of other signals. When those signals are not being received the brain notices. So you get that 'numb' pins and needles sensation following the mental image of what the brain thinks your hand should be doing.
Imagine a train between two cities. The rails are built and unchanging but suddenly one city disappears into a crater. As far as the first city is concerned, the tracks still leave town so ''Send the train!'' And at the end of the day, ''Why hasn't a train come back? It should be here by now.''
When it comes to psychology, energy-working/aura work, or phantom shifting it is a willful practice of meditation and visualization to connect with the idea of the presence of additional limbs (or other body shapes) that never existed in the first place. 'Phantom shift' is the idea of shifting mental focus towards the presence of the phenomenon. 'Phantim limbs' is the experience that comes from that shift in focus.