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This study is a continuation of the combined experimental and numerical investigation [1] of the flow of the eutectic GaInSn alloy inside a cylindrical vessel exposed to a constant electrical current. The emerging electrovortex flow driven by the interaction of the current, which is applied through a tapered electrode, with its own magnetic field might have both detrimental and advantageous effects in liquid metal batteries. While the former work [1] was mainly concerned with time-averaged results, this paper focuses on the transient behaviour of the electrovortex flow which becomes most relevant under the influence of an external axial field. The additional Lorentz force generated by the interaction of the imposed current with the vertical component of the geomagnetic field bz drives the ordinary electrovortex jet flow into a swirling motion. Velocity distributions and motion characteristics, such as spiral streamlines and shortened and irregularly swinging jet regions, are investigated. The mechanism is analysed in detail for bz = 25.5 μT. The maximum angular velocity of the rotating jet is basically linearly dependent on bz, at least for the values studied here. A good agreement between the transient simulation and the experimental result is shown.