Now, how exactly did this process address the temperature in, say, bedroom upstairs?
It didn’t. Even though the cold air was being delivered to the bedroom upstairs, the temperature in it could have fallen just a little bit (for example, if you live in Arizona, the bedroom has a southern exposure, and it is a nice summer afternoon) before the temperature at the point where the thermostat is installed fell below the setpoint. This effect aggravates as the ambient temperature gets close to the setpoint, because in this case the thermostat will be happy almost all the time, but the temperature in problem rooms may drift as far as 10°F apart from the setpoint. The far rooms are starving. And the opposite effect takes place when the ambient temperature is far away from the setpoint because it takes a lot of time for the A/C to satisfy the requirements in the place where the thermostat is installed. By the time it is happy, the far rooms are saturated.