The internal camera (let's be honest and call it the scapegoat camera, because that's the only practical use for human "safety drivers" when they are not permanently engaged) must take almost all its light from IR, because we don't see anything of the smartphone screen glare that the eye movement so clearly hints at.
I don't think the driver is looking at her smartphone. I think she's checking the car's monitor (as in a computer screen). Although to be fair, that should be showing the car's view of its surroundings so I don't know what's going on there.
Edit: Nevermind. Someone posted a picture of the car's interior, below and there's no computer screen.