WIFI assist is a different tool that switches to a cellular network when you do not have or have poor wifi connection. When it switches to cellular you will have charges.

Example from IPhones:

In iOS 9, Apple is giving us the option to choose which connection is best to make a call (Wi-Fi Calling), as well as making iPhones able to switch back and forth in a way that’s both automatic and seamless (Wi-Fi Assist).

[/i]
iOS 9 will also include Wi-Fi Assist, a feature that automatically boosts your connection by relying on a cell signal when your Wi-Fi is weak.

Complaint re: charges:

[i]Is anyone else having a complaint about WiFi assist on iPhone 6? I am a new customer and was charged overages due to this. I was unaware of this needing to be turned off in order of not getting overages.

It is VERY important to put your phone in airplane mode and keep it there. Otherwise there may be charges. WIFI assist cannot work in airplane mode

Also I made three wifi calls to a rental owner from MA to France and there were zero charges. Should be no different calling to a location on SXM...NOT with wifi assist enabled though.This, again, is with Verizon AND on airplane mode.