We present a theoretical framework to understand the collective dynamics of an ensemble of electrophoret-ically driven colloidal particles that are forced to assemble around a single topological defect in a nematicliquid crystal by an alternating current electric field. Our generic model combines phoretic propulsion withelectrostatic interactions and liquid-crystal-mediated hydrodynamics, which are effectively cast into a long-rangeinterparticle repulsion, while nematic elasticity plays a subdominant role. Simulations based on this modelfully capture the collective organization process observed in the experiments and other striking effects as theemergence of conformal ordering and a nearly frequency-independent repulsive interaction above 10 Hz. Ourresults demonstrate the importance of hydrodynamic interactions on the assembly of driven microscale matter inanisotropic media.