The Valve Index does not do reprojection on the device. It does not even do tracking on the device.

It does it on the PC?

SteamVR’s tracking page[1] explains it a little. The HMD is really just displays, radios to talk the controllers (standalone trackers will just have a dongle, runs the same firmware iirc), and its own chip to talk to its own tracking sensors. All the tracking stuff amounts to timing information which is screamed over USB to the PC which does all the math to figure out where you are.

A bulk of this (really interesting!) information can be found on their HDK documentation, but that requires you to sign up with Steamworks.

[1]: https://partner.steamgames.com/vrlicensing

Yes, the runtime handles interpreting the sensor data collected by the device to compute the position and orientation they are in space. The compositor will reproject the next frame it sends to the headset if the application producing the frames does not submit frames before the deadline.