If, say, a particle with energy $E
Answer
Isn't the whole point here that one cannot say where the particle IS exactly? One can only calculate the probabilities of it being at one place.
Tunneling means the probability of it being inside the barrier isn't zero (since we want the probability distrubition to be continuous). There is always penetration of the wave function into the barrier.
IMHO tunneling means the penetration goes deep enough to actually reach the other side, so the wave function of the particle is propagated further on that side too, meaning there's a chance the particle went through. During the passing the particle has had a chance of being inside the barrier.
I don't know if it's correct to say that when the particle has passed, it has been inside the barrier, but that just because the notion of the particle actually being somewhere is somewhat wrong.
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