If you ever have issues with games not picking up your Steam Controller correctly, you should probably take a look at the excellent SC Controller [GitHub] project.
The latest release v0.4.4, that was made available yesterday adds in some interesting new features. A pretty important one, is the new "relative joystick camera" mode, which acts just like the Joystick Camera mode on Steam. Some games (like twin-stick shooters) don't always hold the position of your thumb on the right pad to continually fire, this mode should fix it for games where it doesn't work as expected.
You can also now map triggers to mouse movement, the trackball mode has been extended so it can now be combined with more output modes, an optional tolerance to gesture recognition, an option to map tilting on yaw axis and also per-controller configuration for default menu buttons.
It also fixes PS4 controller compatibility on Kernel versions 4.17+, enables controlling menus with the PS4 D-pad, blacklists some gamepads that have issues with HID and more.
Check it out on GitHub.