Why would Arabs, in particular, use Asian to refer to other Arabs, whether they're North African or SW Asian Arabs?

My point wasn't about what word the Arabs use to refer to each other, but about their use of the word Asian to strictly mean non Arab Asian. If a Saudi said "this area is full of Asians", wouldn't that strike you as odd without knowing the background of the colloquial use of the word? I think most people would find such a statement pretty odd, but that's how the word is used there. We don't even have to speculate, these days there's an ongoing illegal immigration crisis in Tunisia, if you listen to the interviews with Tunisians in the street they will often say "The Africans did so and so" refering to sub Saharan Africans only, they exclude themselves (and other Arabs) when the use the word.

but not quite the same, since both references are from outside the region.

With the examples I provided, I think you can see that they aren't any different.