Yeah, the thing Asians notice about westerners the most is "giant schnozz". So a westerner is indicated in a cartoon by having a huge/blocky hooter and blue eyes, and talking funny. They actually draw the eyes the same on both asians and westerners. It seems to be a asymmetrical thing: westerners notice the eye difference, and draw the noses the same, asians notice the nose difference, and draw the eyes the same.
The core thing to understand here is the concept of "The Other". Groups lock onto specific traits of otherness, and those traits are used as a short-hand to generalize a foreign group. But the foreign group themselves don't necessarily view themselves as adhering to our stereotypes of them. To them, we are the other, and they have specific traits that they identify as meaning "those white guys". If a character lacks any of the "white guy" tropes, they're viewed as probably Japanese, just like americans view characters as probably American if they lack any of the "asian guy" tropes. An elightening example is Marg Simpson. Everyone assumes she's white, even though she's a yellow person with an affro. Because she lacks the package of traits we associate with a specific race. Since Marg Simpson has no race, we assume she's "us" automatically. Similarly, anime characters with giant eyes and weird hair colors don't look like the cliche of "an american" to a Japanese person, so they assume they're Japanese unless told otherwise.
Another an example would be an American cartoon depicting a "French" character. They'd have a pile of cliched "french" things such as a beret, stripy shirt, cigarette holder, and a loaf of french bread. Whereas in France that would just be silly to do, characters are assumed to be French unless you give them a ten-gallon hat, cowboy boots, six-shooter and waving an American flag.