The origin of the uniform Dzyaloshinskii-Moriya interaction (DMI), which is responsible for the creation of chiral magnetism, has been the subject of extensive research. Recently, modern technology has allowed for its production and utilization in a modulated form. Not only can magnetic phases of spin chains be enriched by the presence of such a potential as detailed in Japaridze et al. [Phys. Rev. E 104, 014134 (2021)10.1103/PhysRevE.104.014134], but the capacity of such systems for information transmission is also greatly enhanced. The current paper examines the impact of a staggered pattern of DMI (STDMI) on a chain with a substrate XX Heisenberg interaction. It is demonstrated how enhancing the intensity of this coupling improves the propagation of an entangled quantum state. Additionally, as our analysis has shown, the initial condition over the system's state has a profound effect on the speed at which entanglement spreads. The aberrant behavior of the entanglement's speed profile in response to fine-tuning of the phase factor which adjusts the initial state is the focus of this paper. This anomalous behavior is characterized by dramatic drops in speed for certain phase factor values. We have also shown that, using wave interference principles, we can predict exactly why these phenomena occur. This research will pave the way for additional studies on STDMI and its potential applications in the field of quantum information.