Dynamics of a centrifuged system of two immiscible liquids in a rotating cylinder is studied experimentally. In experiments, the liquids fill a horizontal cylindrical container with transparent walls that rotates about its axis. The study is carried out in the case of fast rotation when under the action of the centrifugal force the light liquid forms an axi-symmetric column on the container axis (core), while the heavy liquid is distributed along the cylindrical wall (annulus). The gravity makes the core shift radially by a small distance, which is practically invariant along the axis. This effect excites the tangential oscillations of the interface leading to the generation of azimuthal steady flows in the rotating frame of reference and to the differential rotation of the interface. The profile of azimuthal velocity has a "discontiunity", which appears on the limits of a viscous boundary layer formed at the interface. The maximum velocity is observed in the outer liquid near the interface. The analysis of the velocity profiles reveals that the liquid-liquid interface is the essential generator of the azimuthal flow in the annulus, while the Ekman pumping appears to affect the flow velocity inside the core. The results of the study may be helpful for the determination of the distribution of inclusions or species on the rotating interface.