If the yellowing occurs only where you are working...ie the sizing
spot... then the solder or the stock you use to size the ring might
be the culprit.
My best guess though is you are experiencing the problem associated
with rhodium plated merchandise from the factory. After sizing you
obviously need to polish, which removes the rhodium finish in that
area. You'll need to polish and re-rhoduim the whole piece for the
same bright white look.
A rhodium set up is not complicated but can initially cost some $ to
the store. You'll need a rectifier, beaker, plating anode, and
rhodium. The rhodium is the most expensive component but should last
a long time as long as you don't contaminate it.
Check out stuller and ask them about your options and safety issues.
You don't need a large rectifier for doing repairs.
With chains you will have a more difficult time getting the plating
to come out well. A good fire coat on the chain and restricting the
area of heat as best as possible will help so you can do a touch up
polish of just that area.