The computer does not know that you fulled up on new fuel. All it does is constantly detect knock and adjust the timing to the optimal level allowed depending on the anti-knock properties of the fuel. It is adjusting timing many times each cycle and even adjust timing of each individual cylinder so it is instant rather than a few tanks.
The reason why it may not be felt until a few tanks is probably because you filled up with several gallons of regular fuel still in the tank so it is blended fuel rather than all premium.
