How does it work exactly?

Try this: Power your car On (not ready) and reset the trip odo to zero. Now go to Ready mode and drive your cold started Prius v 1.7 miles. You'll see less than 40 mpg, possibly less than that.
Without plug-in capability it's a zero sum game with the gasoline. The only battery charge you have came from burning gas and will have to burn gas again to replenish it.
Electric motoring is a tool that your hybrid uses to maximize what you get out of the engine but it won't help you avoid the inefficiency of a cold ICE (internal combustion engine).

 

Prius v driver here, Lots of hills on my 26km round trip commute(1000 feet above sea level, to sea level and back again). When not commuting I do very short trips up and down the same hills about half my commute distance, to grab groceries and such. Granted the weather has been Cold and rainy lately and my latest fill up is averaging 35 mpg in 150km. Based on fuelly.com I reckon if I was driving a normal Prius in the same conditions I'd be averaging 42mpg.
Ymmv, but to put things in perspective, my neighbour with his Ford Fusion V6 averages 18mpg in the same conditions.
Occasionally when I take long trips on the highway I can easily achieve 45mpg in my Prius wagon. My opnion, short trips are worst case scenario for fuel economy in any car but the Prius still does better than a normal car.

 

The PiP can accelerate faster on EV than a regular Prius can in EV PWR mode. PiP is more than sufficient for his driving style. The only reason to suggest Energi or Volt is longer EV range. His range is only 3.4 miles round trip. PiP can easily do that.

 

Typically, my prius 4 runs at about 46-48 MPG (calculated) for 65 mile daily hwy (some stop and go) commute. When I gas up, I have about a 2 mile run home, of typical neighborhood driving. The indicated economy during that drive, including the first mile or so until getting on the hwy the next morning, is about 34 mpg. I find that the mpg calculator is about 5% off to the optimistic side, across the board. Once we get on the highway, the variation in stop and go vs consistency makes almost no difference in economy. The cold weather penalty seems to be about 5%.
The car is driven like a gas car with no particular effort given to increase economy.