Hey Eric, this took a while but here's some more info:
For the Vive controllers SteamVR decides what is treated as left vs. right based on the relative position of the controllers compared to the headset. The controller further most to the left is assigned the left hand role, the other one then is the right one.
This assignment is kept until SteamVR is restarted or at least one controller controller goes off and switches "sides" as soon as the other is turned on (the same check is run once both controllers are turned on).
There were some really really old game engine integrations for SteamVR that decided that the first controller turned on is the left controller, though. I'm not sure if that is the case for any of the titles you mentioned (or any other release nowadays).