It's close enough as to make me wonder if it's an in-universe translation issue or Rothfuss got it backwards. The key to a good headbutt is to hit the soft parts of your opponent's head with the hard parts of yours, which would be the opposite of Tempi's technique. One defense against a headbutt is to simply get your head lower so that the incoming headbutt will have a soft part of the attacker's face (such as their nose) strike a hard part of yours (such as the top of your head). It even works, albeit to a lesser degree, by using the pointer bits of the skull against hard flat surfaces of the head, such as catching their incoming forehead at the edge where the skull start to flatten on top, or catching their jaw on the forehead (although, if they hit mouth-first, there's a decent chance of you getting lacerations from the teeth, often in the form of shrapnel if they hit hard enough).
The philtrum is a notably sensitive part of the face, possibly due to its role in the nursing reflex. If you ever want to prove it, have someone place their finger against your philtrum, as if they were trying to stop a sneeze, then try to walk forward. The pressure will create pain, which is surprisingly effective at stopping forward motion.
Thus, either Tempi is giving bad advice, physiology works differently in their universe, it's a translation issue where he meant one thing, but said another, or it's a matter of Kvothe unintentionally or intentionally fudging the details (much like how MacGuyver episodes always skipped vital elements whenever doing anything explosive) in the retelling.
Ah, and rereading, it looks like it might have been a misunderstanding on the part of the querent:
“But what I saw today,” I said. “Your nose did not break when struck with a man’s head. That is no natural thing.”
Tempi shook his head as he climbed to his feet. “Come. Stand.”
I stood, and Tempi stepped close to me. “Striking with the head is clever. It is quick. Can startle if opponent is not ready. But I am not not ready.”
He stepped closer still, until we were almost touching chests. “You are the loud man,” he said. “Your head is hard. My nose is soft.” He reached out and took hold of my head with both his hands. “You want this.” He brought my head down, slowly, until my forehead pressed his nose.
Tempi let go of my head. “Striking with the head is quick. For me, little time. Can I move?” He moved my head down as he pulled away, and this time my forehead came into contact with his mouth instead, as if he were giving me a kiss. “This is not good. The mouth is soft.”
He tipped my head back again. “If I am very fast . . .” He took a full step back and brought my head down farther, until my forehead touched his chest. He let me go and I stood back up. “This is still not good. My chest is not soft. But this man has a head harder than many.” His eyes twinkled a little, and I chuckled, realizing he had made a joke.
“So.” Tempi said, stepping back to where we were before. “What can Tempi do?” He motioned. “Strike with the head. Slow. I show.”
Vaguely nervous, I brought my head down slowly, as if trying to break his nose.
Matching my slow speed, Tempi leaned forward and tucked his chin a bit. It wasn’t much of a change, but this time as I brought my head down, my nose met the top of his head.
Tempi stepped back. “See? Cleverness. Not mad-thinking word fire.”