The recently proposed orthogonal delay-Doppler division multiplexing (ODDM) modulation has been demonstrated to enjoy excellent reliability over doubly-dispersive channels. However, most of the prior analysis tends to ignore the interactive dispersion caused by the wideband property of ODDM signal, which possibly leads to performance degradation. To solve this problem, we investigate the input-output relation of ODDM systems considering the wideband effect, which is also known as the Doppler squint effect (DSE) in the literature. The extra delay-Doppler (DD) dispersion caused by the DSE is first explicitly explained by employing the time-variant frequency response of multipath channels. Its characterization is then derived for both reduced cyclic prefix (RCP) and zero padded (ZP)-based wideband ODDM systems, where the extra DD spread and more complicated power leakage outside the peak region are presented theoretically. Numerical results are finally provided to confirm the significance of DSE. The derivations in this paper are beneficial for developing accurate signal processing techniques in ODDM-based integrated sensing and communication systems.