The extra free year seems to be valid with most VISA, Master cards. Only VISA has something that is called VISA PERFORMANCE GUARANTEE, usually for platinum card holders and above - but it varies between banks so some 'lower cards' offer it, and some platinum don't.
Before the end of the free second year, you just call VISA and tell them you want to buy the performance guarantee and they'll take care of it for you. Here's some more info:
http://usa.visa.com/personal/cards/credit/visa_signature_benefits_wm.html?it=c|/personal/cards/benefits/index.html|Warranty%20Manager%20Service
My provider is amazon/chase too and, as stated, the automatic double warranty feature is free and automatic without registration. Subsequent coverage under the performance guarantee program costs depend on the original purchase price of the item and is paid once, not monthly.