I managed to solve it and it was also quite simple:
Just changed the SDK from Oculus Rift Standalone to Gear VR, in the script VRTK_SDKSetup (SDK Selection), usually located in the object [VRTK_SDKManager] > [VRTK_SDKSetups] > Oculus, inside the Scene.
EDIT: Actually, in the end I had to create a custom script to bridge VRTK 3.3.0 and Oculus new APIs.
I put it on GitHub in case anyone needs it. It's not very well written, but it works.