I can't remember the exact chemical reactions that are occurring, but basically the tarnish/oxidation is being taken off the silver and onto the aluminum foil if I recall correctly. (Hence why if you look at the foil after you're done, you'll probably notice some discoloration particularly around the water line.
I've used this method with hot water and baking soda for awhile with good results, mainly on my mouthpieces and occasionally when cleaning my euphonium I'll use the same method with the parts that are silver plated, solid machined brass (valve caps/bottoms, and buttons). Works really well for getting into the little grooves/ridges of those parts, which can be a pain to use polish on!
I would be wary of using this on any parts of a horn that isn't silver or silverplate, as I think this method is specific to silver. (Again having to do with the chemistry that I'm admittedly not as familiar with as I would like!)
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)