Inside all SteamVR games I've tried so far - like "I Expect You To Die" and "Until You Fall", which both support Oculus Touch controllers officially - my controllers show up as Vive Controllers and that also makes the controls kind of messed up (since they work a tad bit differently from each other).
When I use SteamVR via ALVR on the other hand, the controllers show up correctly as Oculus Touch. It's easiest to see this in "I Expect You To Die" because in the very first screen it asks you to choose whether you want to use the Mouse or a VR controllers, and on Oculus Link I get shown a Vive Controller, and on ALVR I get shown a Oculus Touch controller.
Confusingly, inside SteamVR Home, the correct Oculus Touch controllers show up even over Link. But for the games, the wrong thing is displayed somehow. Did anyone else have this problem and know how to fix it?