A quasiclassical analysis of the differential inelastic scattering of oriented [Formula Presented] atoms on He at a collision energy of 1 eV is presented. Inelastic channels correspond to spin-changing events populating different Zeeman sublevels of three fine-structure states of [Formula Presented] [Formula Presented] 1, and 2. The magnitude of the right-left scattering asymmetry in the helicopter plane is shown to depend on the locking dynamics. The relative values of different Zeeman-specific cross sections are determined by the diffraction scattering on the attractive [Formula Presented] state in the entrance channels, by the Coriolis mixing between degenerate components of the repulsive [Formula Presented] intermediate state, and by the radial coupling between 1-1 and [Formula Presented] fine-structure components of the [Formula Presented] states in the exit channels. The predicted large right-left scattering asymmetry suggests that it can be measured experimentally.