What's your current camera control rotation setup (mainly the input stuff)?
I'm currently using a setup like this:
- rotation input change: 90
- use delta time: enabled (i.e. it'll rotate 90 degrees per second)
- use axis: enabled
- axis key: your input key for the right thumbstick
For the input key, sticks are coming from the Unity Input Manager (or using extensions for e.g. Unity Input Action support). In this case it's crucial to enable the Is Joypad Axis setting and using Hold input handling (to keep getting the input).