My other Fiat does the exact same thing and it's not a fault. You were not supposed to press the accelerator when changing the gears because it is totally unnecassary. Idle speed is controlled by the computer. It will not stall, don't worry.
Also when you want the car to go very slowly, just release the clutch and don't press the accelerator. Very useful for parking the car. However, I believe that the car learns to compensate the pedal movement and sometimes it can be quite unexpected. So a little touch on the pedal in 1st gear can make the car accelerate. All this behaviour changes when the car reaches operating temperature, then it gives full control of the throttle. I thought that it must be a fault, but no, it really is how these electric throttles work and it just takes a little time to get used to it.