Proteins can form membraneless condensates that regulate cellular processes, often wetting intracellular surfaces like membranes and cytoskeletal structures. However, the underlying physical principles of this interaction remain poorly understood. To explore this, we study Tau, an intrinsically disordered, microtubule-associated protein linked to neurodegenerative disorders. Tau can form phase-separated condensates and, at low concentrations, assemble as non-uniform islands on microtubules. It binds in two modes: a thin adsorbed layer or a thick, multi-layered envelope. We use a lattice gas model to show that this behaviour can be understood as surface-induced condensation. We show that a heterogeneous microtubule surface gives rise to such islands and that this heterogeneity is attributable to the post-translational modifications of tubulin. We speculate that Tau condensation on microtubules can be harnessed by cells to regulate diverse microtubule-based molecular pathways spatially.