Many systems regulating cell polarity involve stable landmarks defined by internal cues. In the rod-shaped fission yeast Schizosaccharomyces pombe, microtubules regulate polarized vegetative growth via a landmark involving the protein Tea1. Tea1 is delivered to cell tips as packets of molecules associated with growing microtubule ends and anchored at the plasma membrane via a mechanism involving interaction with the membrane protein Mod5. Tea1 and Mod5 are highly concentrated in clusters at cell tips in a mutually dependent manner, but how the Tea1-Mod5 interaction contributes mechanistically to generating a stable landmark is not understood. Here, we use live-cell imaging, FRAP, and computational modeling to dissect dynamics of the Tea1-Mod5 interaction. Surprisingly, we find that Tea1 and Mod5 exhibit distinctly different turnover rates at cell tips. Our data and modeling suggest that rather than acting simply as a Tea1 receptor or as a molecular "glue" to retain Tea1, Mod5 functions catalytically to stimulate incorporation of Tea1 into a stable tip-associated cluster network. The model also suggests an emergent self-focusing property of the Tea1-Mod5 cluster network, which can increase the fidelity of polarized growth.