We investigate the quarkonia correlators and spectral functions in gluonic QCD within a potential model with different screened potentials. We compare the obtained temperature dependence of charmonium and bottomonium correlators with lattice data. Our results are in qualitative agreement, namely, the 1P states corresponding to the scalar and axialvector channels dissolve right above the deconfinement temperature, whereas in the pseudo-scalar and vector channels we see that their survival up to at least 1.5 Tc with almost no change in their properties. However, we identify a significant temperature dependence of the correlators from the thermal modifications of the continuum, feature not detected on the lattice. Furthermore, we concentrate on understanding why the behavior of the eta_c and the J/psi correlators differs significantly at large distances. We suggest that this difference is due to the contributions from charge fluctuation and transport effects to the vector correlator.