We examine the evolution of buoyant axisymmetric plumes as they are influenced by background rotation in a uniform density ambient fluid. The source Rossby number is sufficiently large that rotation does not directly affect the plume at early times. However, on a time scale on the order of half a rotation period, the plume becomes deflected from the vertical axis. For some experiments and simulations, the deflection persists and the flow precesses about the vertical axis. In other cases, shortly after being deflected, the plume laminarizes near the source to form a near-vertical columnar vortex, which we refer to as a ``tornado''. Tornado formation is intermittent, appearing in some experiments and not in others even if the source and background rotation parameters are identical. Simulations reveal that this is a consequence of competing dynamics that occur on comparable time-scales. As a consequence of entrainment, vertical vorticity builds up within the plume reducing the Rossby number and suppressing vertical motion at distances progressively closer to the source. Meanwhile, the azimuthal flow around the vicinity of the source increases, which acts to suppress turbulence in the near-source flow. Although the former process ultimately acts to deflect the plume off-axis, in some instances the swirl around the source succeeds in laminarizing the flow, resulting in tornado formation. Experiments and simulations show that tornado formation is more likely if the plume at the source is ``lazy'', meaning it has a deficit of momentum with respect to buoyancy compared with that for a pure plume.