there's no acceleration relative to the space station, which in turn means a zero reading on the phone's sensors.

I'm pretty sure this - and the OP - are wrong. But perhaps I'm missing something.

We all agree that gravity still effects the station/astronaut/phone right? Gravity is pulling on those things, changing the direction of their velocity, and resulting in a circular/elliptical orbit, right?

Then what does "relative to the space station" have to do with anything? Don't get me wrong, I get that - to an astronaut - relative to the station means it feels like 0g. But the phone doesn't have a clue about anything to do with a space station.

If you took the phone out of the space station and held it up as you watched the surface of the Earth flying by, the phone wouldn't suddenly "realize" it's moving again, and start working. It would work the whole time, because it doesn't get a reading "relative to the space station." It detects acceleration, just like on the surface of the Earth (although to a lesser extent, since gravity is inversely proportional to distance), it detects the gravity of the Earth.