An Adept's "aura" (just like that of anyone else) extends beyond whatever clothes and armor they're wearing. It's why a mage can still cast a line-of-sight spell at someone who's all wrapped up in clothing or milspec armor, without seeing their skin they can still see the person to target them with their intent to cause damage (or heal, or confuse, or whatever). A metahuman aura, whether it's being read, or manipulated, extends past what they're wearing so that a mage's intent can affect it.
Ditto, with an Adept and his aura; so his ability to inflict magical damage via Killing Hands (which, keep in mind, is just a flavor name, they can do lethal damage with kicks, knees, elbows, etc) extends, along with his aura, beyond whatever clothing or armor he's wearing.
Rules-wise, he's kosher. Game balance wise? It sounds like you're concerned he's upsetting how things are working at your table. Maybe you should have a little talk with him and ask him to tone it down a little, maybe you should ask him why he feels he needs to try so hard to be able to take those kind of hits, maybe you should look at what other over-the-top gear the rest of the party might be sporting, or maybe you should look at the overall "feel" of your game (if folks are stomping around in heavy milspec armor, and you don't mean for the game to feel that way, how did it get off the rails and does it bother you enough to try and make a change?).