If you show us the solver and CVX output, we can say more. You may get that warning message whether or not the successive approximation method was used. But we can tell whether it actually was used by seeing the output.
As general advice, if you have Mosek available, use that as solver, with CVX 2.2. Otherwise, follow the advice at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions
What evidence do you have that the CVX results are not right?