I'm not sure if I can answer your question other than to say "the wrong way of calculating the coefficients will give the wrong answer, whereas the right way will give the right answer". You stated that you calculated the coefficients of the Hamiltonian in second quantized form. These are the coefficients that AutoMPO expects to be used to define the Hamiltonian, since it is also working in the second quantized formalism. Any other coefficients will, by definition, give a different Hamiltonian, include other coefficients obtained by antisymmetrization.
So it's really more up to you to tell me why you think that antisymmetrization is needed for Hamiltonian coefficients? It is not a requirement for a fermion Hamiltonian. Rather the requirement is that the Hamiltonian is Hermitian.
Hope that helps!