I don't have a 500e yet, but based on what I know I would say thin tires plays a role. Wider tires and all-season tires with rain channels reduce the chances of hydroplaning. The other issue is that EVs, hybrids, and diesel powered vehicles produce a lot of low-end torque…instant torque in the case of an EV. Gobs of torque with an open differential can definitely give you a less confident feel, but the electronic traction control and stability control should be more than enough to keep your Fiat driving in the direction you want.
I guess I'd have to drive a 500e or specifically yours to determine the issue. Just take it slow and don't be a hero. We get rightfully criticized by out of staters because southern Californian, in general, really don't drive well in the rain at all.