The polarized components of transmission spectrum of a multilayered photonic structure containing a nematic liquid crystal under the magnetic-field-induced torsion deformation have been investigated. Since the planarly twisted director structure of the nematic is unrelated to a decrease in its optical anisotropy, the control of the polarization and spectral characteristics of the eigenmodes is based on the occurrence of a geometric phase, whose contribution gradually increases upon nematic deformation. Along with the previously observed blue shift of the cavity o modes, the anomalous shift of the cavity e modes to the long-wavelength region (red shift) of the transmission spectrum has been detected. It has been shown that the countershift of the modes narrows the intermode interval. Remarkably, the extremal approaching of e and o modes in magnetic field H_{ex} occurs below the avoided crossing phenomenon observed in the stronger equalization field H_{eq} (H_{ex}<H_{eq}). The experimental results have been interpreted by the numerical simulation of the transmission spectra of the chiral photonic structure using the transfer matrix method.