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Analytical investigations are carried out for the soliton propagation and reflection in a magnetized positive-ion-negative-ion plasma having two types of electrons based on the reductive perturbation technique. It is found that this type of plasma does not support rarefactive solitons, which are otherwise found to propagate in negative-ion-containing plasmas with isothermal electrons. This is the consequence of the low-temperature electron component present in the plasma. Two types of compressive solitons, namely, the fast wave soliton and the slow wave soliton, are found to exist, but only the fast compressive solitons will reflect. The effect of ion temperature is to enhance the soliton reflection; the same is the case for an increased number of negative ions. However, the effect of low-temperature electrons is to weaken the soliton reflection. Interestingly, the solitons are found to downshift after their reflection, and this shift is less under the effects of stronger magnetic field, smaller wave propagation angle, and a higher concentration of low-temperature electrons. However, larger amplitude solitons are more downshifted, and the shift is more for higher ion temperature and when the wave propagates with larger phase velocity.