Almost all commercially sold (rather than studio jeweller / handmade) jewellery is plated before sale. It saves on polishing and finishing costs and hides any firescale, oxidisation, or tarnish without having to do to any thing aggressive or time consuming. In the case of silver, it's usually plated with fine silver to give a very bright appearance. Over time, that plating wears off, exposing the bare silver underneath, which is then vulnerable to tarnish. This can be restored to an extent with a magnetic polisher or tumbler, but I, and many others, actually prefer the appearance of silver that has aged naturally, giving a more interesting depth to the finish rather than the overpolished ultra shiny 'new' look.

If you want to clean the less easy to reach parts of links, you can go a long way with a cheap ultrasonic toothbrush and some silver dip. A tumbler or polisher is always going to be limited by the size of the media it uses.