Engineering gauge fields in synthetic dimensions provides a useful framework for studying quantum interference associated with effective synthetic flux and coherent population dynamics. We study a spectral phase control scheme for tuning the effective synthetic flux in a finite synthetic structure formed by two hyperfine levels in the ground electronic state and two hyperfine levels in the excited electronic state of ultracold ⁸⁷Rb atoms on the D₁ line. These four levels form a four site closed diamond loop, which serves as a minimal physical model for examining an interference mechanism analogous to Aharonov Bohm caging. The loop is driven by a broadband laser pulse field shaped by spectral phase, whose spectrum covers the relevant hyperfine splittings, so that several transitions allowed by electric dipole selection rules are addressed coherently by the same optical field. By solving the time dependent Schrödinger equation and analyzing the closed loop phase associated with the four optical couplings, we examine how spectral phase modulation changes the effective loop flux and affects the interference between two photon Raman transition pathways. Numerical simulations show that changing the spectral phase can switch the dynamics between population suppression caused by destructive interference and coherent population transfer. In the absence of externally imposed spectral phase modulation, the four level loop exhibits an intrinsic effective π synthetic flux, which originates from the relative sign structure of the electric dipole transition matrix elements. Under this condition, the competing Raman transition amplitudes interfere destructively, leading to suppression of the target state population and confinement of the dynamics within a restricted energy level subspace. Furthermore, this population confinement induced by destructive interference exhibits robustness with respect to variations in pulse bandwidth and single photon detuning. The results clarify how the dipole sign structure can generate an intrinsic loop phase and how spectral phase shaping can tune the associated synthetic flux. This study provides a theoretical approach for controlling effective gauge fields in synthetic dimensions and coherently manipulating multilevel quantum systems through spectral phase shaping of broadband pulse fields.