Gasoline is a mix of light hydrocarbons, and it is meant to vaporize quickly. In countries where winters are harsh, gasoline is even lighter than the one fabricated in warmer places; that is done to prevent the formation of hydrocarbon crystals in the gasoline (the temperature in which those crystals begin to form is called "cloud point"). Small amounts of gasoline evaporate fast on your hand because of your body's warmth and the large superficial area of the spill, but if you pour some amount of gasoline into a glass and leave it in contact with the air, there will be no more gasoline left after some time.
The "white residue" is your dry skin, because gasoline washes out your skin's natural oils.
You shouldn't be concerned about occasional gasoline spills on your skin as it doesn't penetrate too deeply into your body, but constant contact with the product may irritate your skin.