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The electrostatic response of the edge plasma to a magnetic island induced by resonant magnetic perturbations to the plasma edge of the circular limiter tokamak TEXTOR is analyzed. Measurements of plasma potential are interpreted by simulations with the Hamiltonian guiding center code Orbit. We find a strong correlation between the magnetic field topology and the poloidal modulation of the measured plasma potential. The ion and electron drifts yield a predominantly electron driven radial diffusion when approaching the island X-point while ion diffusivities are generally an order of magnitude smaller. This causes a strong radial electric field structure pointing outward from the island O-point. The good agreement found between measured and modeled plasma potential connected to the enhanced radial particle diffusivities supports that a magnetic island in the edge of a tokamak plasma can act as convective cell. We show in detail that the particular, non-ambipolar drifts of electrons and ions in a 3D magnetic topology account for these effects. An analytical model for the plasma potential is implemented in the code Orbit, and analyses of ion and electron radial diffusion show that both ion- and electron-dominated transport regimes can exist, which are known as ion and electron root solutions in stellarators. This finding and comparison with reversed field pinch studies and stellarator literature suggest that the role of magnetic islands as convective cells and hence as major radial particle transport drivers could be a generic mechanism in 3D plasma boundary layers.