Treadwear warranties:
In theory, if a claim for treadwear warranty is accepted and there is a prorated adjustment, the transaction is over.
Put another way, you have been compensated for what you didn't get and the next set of tires starts the process over.
Example: Your first set of tires achieves only 50% of the warranty mileage, so you get a 50% discount on the next set of tires. That transaction completely resolves any issues - except what happens to the set going on - which will be dealt with when you get there.
Also, I want to point out that OE tires - that is, the tires that come on a new car from the assembly plant do NOT have a treadwear warranty - even if the tire is advertised for sale with one. That's because the vehicle manufacturers only buy the tire and not the treadwear warranty coverage - where the tire is sold on the open market has the treadwear warranty cost rolled into the purchase price.