Temperature and field-dependent neutron powder diffraction (NPD) measurements have been performed to reveal the nature of the unusual evolution of the magnetoresistance behavior with increasing Fe content in the intercalated compounds FexTiS2 (with x = 0.25, 0.33, 0.50, 0.55) synthesized by solid-phase reaction method with prolonged homogenization heat treatment. As derived from neutron diffraction measurements, both the Fe0.25TiS2 and the Fe0.50TiS2 compound exhibit an antiferromagnetic (AFM) order below their respective Neel temperatures T-N approximate to 52 K and T-N approximate to 140 K, which results in the presence of a large magnetoresistance accompanying the field-induced phase transition from AFM to the ferromagnetic (FM) state. At low temperatures, this AFM-FM transition is irreversible, confirmed by the irreversibility of changes in the NPD patterns and the presence of remnant magnetoresistance. In contrast, Fe0.33TiS2 shows short-range magnetic order at T-f approximate to 44 K due to a triangular network of intercalated Fe atoms and frustrations of exchange interactions with a field-induced FM alignment of Fe magnetic moments in an applied magnetic field as revealed by NPD measurements. The field-induced transformations of the cluster glass magnetic state in this compound lead to a significant decrease in electrical resistivity. According to NPD data, a reduced impact of an external magnetic field on the electrical resistivity of the compound Fe0.55TiS2 can be ascribed to the presence of ferromagnetic or ferrimagnetic order in compounds with the Fe concentrations above x = 0.50. The results obtained indicate that the distribution of the Fe atoms, along with their concentration in FexTiS2 layered compounds, plays a decisive role in the formation of the magnetic state and the behavior of the magnetoresistance.