The surface of a topological insulator hosts Dirac electronic states with the spin-momentum locking, which constrains spin orientation perpendicular to electron momentum. As a result, collective plasma excitations in the interacting Dirac liquid manifest themselves as coupled charge- and spin-waves. Here we demonstrate that the presence of the spin component enables effective coupling between plasma waves and spin waves at interfaces between the surface of a topological insulator and insulating magnet. Moreover, the helical nature of spin-momentum locking textures provides the phase winding in the coupling between the spin and plasma waves that makes the spectrum of hybridized spin-plasma modes to be topologically nontrivial. We also show that such topological modes lead to a large thermal Hall response.