In this particular case, the clock does not start over IF you move the first fish out of the QT into a clean tank. You still need to maintain copper levels in the original QT for at least 30 days after the introduction of the last fish.
We know that copper quickly kills free swimming ich and prevents it from infecting fish. We also know that the ich can only feed on the fish for a maximum of 7 days. In theory, after 7 days at proper copper levels the fish should be completely free of the parasite.
So why the 30 day treatment then? Lets say that a new ich parasite (called a theront at this stage) infects your fish right before you put it into your QT. It spends a maximum of 7 days feeding on the fish (trophont stage). It leaves the fish as a Protomont (normally only a few hours) and looks for a hard surface on which to reproduce in what is called the tomont stage. Anywhere from 3 to 72 days later the tomonts hatch and release new theronts to start the cycle over.
Copper is most effective at killing ich when it is a theront. After 7 days at proper copper levels this means no new tomonts can be formed, which means no new theronts can be hatched. However, during that first 7 days there may be tomonts that formed and can hatch in that 3 to 72 day window. In proper copper, these new theronts are quickly killed before they can infect a fish. This is why a fish in proper copper levels is clean after 7 days. So why the extra 23 days if the fish is clean at this point? It can take 2 to 3 weeks for the copper to genetically alter the tomonts enough to prevent viable theronts. Once there are no viable tomonts it is safe to remove the copper.
That was the long way of saying that the first 7 days of a 30 day treatment is to get the fish clean. Days 8 through 30 are to keep the fish safe while making sure the tank is clean.
I think we disagree on this and 14 days is my new preference. I feel this offers plenty of wiggle room. I do know some people only treat this way for 9 days which does offer zero wiggle room. With this method, instead of treating the tank, you remove the fish from the tank so that tomonts are not an issue. I also find it easier to maintain proper copper levels for 14 days than it is for 30. The big down side to this method is that you need to set up and maintain 2 complete QT systems with completely separate equipment or you risk cross contamination. Many people find setting up a single QT to be challenging so asking people to set up 2 of them doesn't go over very well.