The optimum conditions for unidirectional coupling in quasi-phase-matched non-Hermitian systems are analyzed for both autonomous and externally driven configurations. The quasi-phasematched coupling mechanism is due to periodic modulation of the real and imaginary parts of the coupling interface, which results in not equal coupling coefficients between interacting waves. The conventional parity-time (PT) symmetry theory suggests that the strongest unidirectionality should occur exactly at the exceptional point (EP). We show that this expectation is in general incorrect, as the optimum is shifted away from the EP depending on the detuning from exact quasi-phase matching resonance. The shift is signed: reversing the detuning moves the optimum to the opposite side of the nominal EP. We formulate a unified two-mode description for autonomous and driven systems, and derive the normal forms governing the displaced observable singularities near the nominal EPs.