
Short answer: Asians dont find it as offensive, but rather see it as a stale and unfunny joke.
Why its more offensive if a caucasian does it is written below.
The implications are different because what happened historically.
Please note that I am canadian, so these facts may slightly differ in america and in europe. I know that racism existed in both places, but i am not educated enough to explain it.
In canada, racism was (and still is to a lesser extent) very prevalent and asians were alienated. Japanese people were segregated, deported, and were called called slurs due to ww2, while chinese people were forced to live in poorer areas (thus became chinatown), and due to the systematically racist government, it was difficult for them to have a decent living. Koreans came much later, but caucasians cant tell them apart so they are lumped into the same category. As racism permeates throughout society, there are people that clearly benefit on the other side of the spectrum. Non asian citizens are easier to sway when they fear and ostracize the "yellow people", and business is easier when anti-asian laws/permits are enforced.
"But what does this have to do with slanted eyes?" Media brainwashes people and make it easier to maintain racism. If asians are constantly shown as greedy, yellown skinned, with slanted eyed miscreants with terrible accents, people begin to believe that thats what asian are. (Obviously thats now true, but racists then and even today believe otherwise)
On the other hand, korea is a largely homogenous asian country. Racism against asians is impossible; theyre the majority demographic. (Note: racism and xenophobia is different. Im aware of the tense relations betwen asian countries.)
Regardless, the slanted eye jokes are generally ill-mannered and unfunny. The difference is between a korean and a caucasian doing it is that korea doesnt have a racist backstory to further tarnish it. Caucasians do.
In a similar way, its kinda like how black people can say the n word but non black people cant. We havent faced the struggles and racism black people went/go through (in fact we're the reason they even struggled in the first place). Its not our place.
Source: A white person who listened during history class.

Usually when Asians pull up the corners of their eyes to mimic other Asians, it's mostly used as like a joke on how the person's eyes look. There's nothing really wrong with it unless it's meant as a racial stereotype. For example, I'm full Chinese but my eyes are bigger than what the stereotype says. Usually caucasians would mock me by pulling up their eyes even when mine aren't slanted or squinted. That would be an offensive sterotype.
When a Caucasian person pulls up on their eyes it's kind of an offensive way to mock Asian people.
What I want to know, however, is what it means when an Asian person does the same thing?
Does it even have a meaning?
A picture in chap 8 made me think of it, so please reference the picture if I'm not being clear.
http://iweb6.mangapicgallery.com/r/newpiclink/unriped_expression/8/2fc2fc83d7db8ff8884b31b742602e0d.jpeg