The Phaedrus seems to be saying that soul is the cause of all movement in an organized world, a world measurable by Time. In a non-organized world not measurable by Time one can wonder whether the movement in question has anything to do with this. At this stage words start to break down under the strain. Plato is compelled to give some description of the pre-cosmic chaos, and talk of movement in such a world is no more and no less intelligible than phrases like 'before this' (53a8) in the same passage, when Time has been admitted to be absent. Plato, as far as I can see, is dealing in two instances with two completely different types of motion, the one accepted and universally admitted, and operating in an organized world of temporal succession, the other a pis aller trying to describe a reality in every sense different. If this analysis is correct, there seems no reason to reproach Plato here with lack of logic, though on points of clarity he may leave a lot to be desired.
Robinson, Thomas M., "The Argument for Immortality in Plato's Phaedrus" (1966). The Society for Ancient Greek Philosophy Newsletter. 235.