In many organisms, positive and negative signals cooperate to position the division site for cytokinesis. In the rod-shaped fission yeast Schizosaccharomyces pombe, symmetric division is achieved through anillin/Mid1-dependent positive cues released from the central nucleus and negative signals from the DYRK-family polarity kinase Pom1 at cell tips. Here we establish that Pom1's kinase activity prevents septation at cell tips even if Mid1 is absent or mislocalized. We also find that Pom1 phosphorylation of F-BAR protein Cdc15, a major scaffold of the division apparatus, disrupts Cdc15's ability to bind membranes and paxillin, Pxl1, thereby inhibiting Cdc15's function in cytokinesis. A Cdc15 mutant carrying phosphomimetic versions of Pom1 sites or deletion of Cdc15 binding partners suppresses division at cell tips in cells lacking both Mid1 and Pom1 signals. Thus, inhibition of Cdc15-scaffolded septum formation at cell poles is a key Pom1 mechanism that ensures medial division.