Basically you ask about the Purple of Cassius test, a test that gives about 9-12 ppb in precision (and +/- a few ppb if done colorometrically with a really great absorption curve)
Tin chloride is kept in acidic conditions because it hydrolyzes to its basic chloride. Tin (II) would really like to go to tin (IV) species, this means it is a good reducing agent, as it becomes oxidized. This is why you should keep a bit of pet ether or xylene on top of your stannous solution if you plan to keep it--also, leave some tin in the bottom, it will further prevent oxidation.
What happens is a redox between solvated, complexed Au (III) and acidic Sn (II). The gold is reduced to its ground state, while tin moves up in oxidation. The gold is in a very, very fine form, below a micron in size if I recall. This sticks to the surface of the formed suspension (technically a colloid) of basic stannic hydroxide which exists with SnCl4 that couples with it a la charge interaction. That nano fine gold on the surface is what makes it the purple color.
There is no real ''official'' complex with it like there is for Pt and the PGMs but that may be argued.