The mpg readout will always start again a the last figure in its memory (ie when you turned the engine off last time), as far as I know this will be the same on any car.
Every car I have ever had has stayed on full for a while after tank has been topped up till the petrol pump cut out, because you have filled the filler pipe to the tank as well, and on the Jazz this goes from filler cap to under the drivers seat, quite a length of pipe!
If you want a truly 'dynamic' readout from the mpg reading I suggest you zero the 'trip mileage' display every time you fill the tank, this will also zero the 'mpg' readout. The mpg reading will now react very quickly to changes in your driving and gradients in the road etc. The more miles you have accumulated on the trip mileage the slower the mpg readout is to react, as the mpg is knid of averaged out over the whole of the figure on the trip mileage. If you stop in traffic the figure on the mpg display will gradually drop as you are using petrol but not going anywhere.
The mpg display is updated about every 10 seconds, and the smoother your driving the neared to actual mpg the readout will be (every time you use the brakes you are wasting fuel, and the harder you brake the more fuel you just wasted).
Remember that in warmer weather your car will use less fuel than in cold weather, so don't be surprised if you get 10 to 15% better mpg in summer than in winter in like-for-like driving.