Fiat's (and most other car makers') current use of the term Hybrid is very misleading.
The first hybrids were the Toyota type, where the car has both a petrol engine (with starter motor) and an electric motor, and a beefy storage battery for the latter. These drive off the electric when they can, but if they need an extra bit of oomph, or the battry's running low, then the petrol starts up and powers the car, and drives an alternator to recharge the battery. Now, to help make this clear, they are called 'self charging hybrids'
Next came 'plug in hybrids' where the battery for the electric motor is charged by plugging the car into the mains, Once the charge is used, that's it - it's all petrol after that. Normally they can manage about 30 miles of pure electric travel. Very few (if any?) plug-in hybrids can partially recharge the battery (eg through regenerative braking) while driving.
Now, Fiat (and others) use the Hybrid badge to woo buyers and appear to be green, but it's only really a 'mild hybrid' . This is little more than normal stop/start, except it 'stops' (the engine cuts out') while the car is still rolling to a stop (i believe, when it drops below 18km/h?), and when pulling away again it basically uses a beefed up starter motor as the initial power, before it starts the petrol engine. So it will feel like any other stop/start but with the extended 'off' (rather than 'stop') period when the electrics briefly do a (tiny) bit of the work. As well as the normal battery under the bonnet, there's a second, very small(!) one, which I think its under the front seat? As mentioned above, the starter is combined with the alternator in one unit. In around town driving, this mild hybrid system can produce a bit of a fuel saving (mostly through turning the engine off a bit sooner, and partly through less weight by combining the starter and alternator, although this is probably cancelled out by the weight of another battery). But on the open road, unlike the original definition of hybrid where the electric and petrol could act together for a surge of power, a mild system will offer no benefit and so no better fuel consumption.
That said, it is a start in the right direction, but I would argue the use of the term hybrid is very misleading...