In eukaryotes, cyclin/CDK complexes drive cells through DNA replication and mitosis, establising cell cycle temporal order. The fission yeast S. pombe is able to function with a single cyclin/CDK complex, with cell cycle order emerging from differential substrate sensitivities to CDK activity. What influence cyclin specificity has upon the cell cycle in this situation is currently unknown. Here we show that in a system that is reliant on a single cyclin for both the G1/S and G2/M transition, cyclin specificity is not needed for the G1/S transition, but instead is required for the G2/M transition and correct localisation of cyclin/CDK to the yeast centrosome equivalent, the SPB. This loss of centrosome localisation was also seen in human cells expressing mutant Cyclin B1, suggesting conservation of function. In fission yeast, although interphase centrosomal localisation is lost, mitotic SPB localisation remains. This hitherto unknown second localisation method is dependent on Polo kinase, suggesting a finer spatiotemporal control of cyclin/CDK during cell cycle progression than previously known. Thus, cyclin specificity is intrinsically twinned with spatial control of cyclin/CDK, and we suggest that this regulation may be conserved through evolution.