As we know ArcRotateCamera.alpha for horizontal rotation, ArcRotateCamera.beta for vertical rotation. How to invert these two controls when using mouse or pointer? MovementX for vertical axis and MovementY for horizontal aixs. 
Ha! I’ve been waiting forever for that question — because this is where legends are born.
To invert the axis direction, you just need this code:
camera.angularSensibilityX = -camera.angularSensibilityX;
(Same trick applies for camera.angularSensibilityY if needed.)
And yes, the names are gloriously bad Frenglish — but hey, they’re legacy now. Part of the dysfunctional family. 