> Can I turn this feature off?

The article says that you can, by disabling CarWings/NissanConnect. Which you should probably do if you're a connected Leaf owner, as it lets anyone control AC/heating and gives them historic driving information (date, distance and "driving efficiency").

> How does it communicate?

Lost the source (maybe one of the forums linked from http://www.troyhunt.com/2016/02/controlling-vehicle-features...) but I read the CarWings service sends an SMS to the car, which contacts the webservice to return its information.