Not quite. 'Asian' in British colloquial usage normally refers to brown-skinned peoples (of any religion) deriving from the Indian sub-continent. 'Asian' would not normally be used of Arabic etc peoples from the Middle East. They would be described as 'Middle Eastern.'
True, but you can’t really distinguish accurately when you see someone in a car or running with a knife... so witness report of “Asian” could suggest either south Asian, Middle Eastern, or North African.