Can your titers for hepatitis b change from negative to positive right after the shot?

Yes: If you were previously vaccinated but lost the hepatitis b surface antibody response over time, the immune system still has a "memory" of it. When you are re-exposed to the vaccine, even many years later, you can have a very quick response. Some people had prior infection but it wasn't recognized because they were not tested for hepatitis b core antibody. They can also have a rapid response.