We establish that the asymptotic mean action and the asymptotic linking number of irrational pseudo-rotations remain well-defined everywhere and constant for every \ (C^1\) irrational pseudo-rotation that behaves as a rotation on the boundary. As a consequence, we demonstrate that the isotopy of irrational pseudo-rotations with a positive rotation number is a right-handed isotopy in the sense of Ghys.
Senior et al. (Sun,) studied this question.