Our system can work alongside Cinemachine and other camera plugins, but to do so you must ensure that it is being executed after those plugins. To do so, open the Script Execution Order tab in your Project Settings, and add the PlanarReflectionRenderer and PlanarReflectionCaster components at the very end of the chain, as in the following image.
After this simple step, the reflections should work without issues with your Cinemachine cameras and transitions.