The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and zeros) that are marked by phase singularities in a complex frequency plane. Here, by using temporal coupled mode theory, we derive analytical expressions allowing to predict the location of these phase singularities in a complex plane and as a result, allowing to control the induced phase modulation of light. In particular, we show that spatial inversion symmetry breaking-implemented herein by controlling the coupling efficiency between input and output radiative channels of two-port components called metasurfaces-lifts the degeneracy of reflection zeros in forward and backward directions, and introduces a complex singularity with a positive imaginary part necessary for a full 2 pi-phase gradient. Our work establishes a general framework to predict and study the response of resonant systems in photonics and metaoptics. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement