(Tm_1-xMn_x)MnO₃ solid solutions were synthesized at a high pressure of 6 GPa and a high temperature of about 1570-1670 K for 2 h for x = 0, 0.1, 0.2, and 0.3. Magnetic, dielectric, and neutron diffraction measurements revealed that the introduction of magnetic Mn²⁺ cations into the A site leads to an incommensurate spin structure for x = 0.1 and to a ferrimagnetic structure for x ≥ 0.2. Commensurate magnetic structures have a much larger correlation length (∼400nm for x = 0, ∼600nm for x = 0.3) than the incommensurate magnetic structure (∼12nm for x = 0.1). The presence of Tm³⁺ and Mn²⁺ (with different sizes) at the A site causes significant microstrain effects along the a direction which are absent for x = 0 and get stronger with increasing x. Magnetic ordering occurs at the Néel temperature T_N = 37 K (x = 0.1) and at the ferrimagnetic Curie temperatures T_C = 75 K (x = 0.2) and T_C = 104 K (x = 0.3). Ordering of magnetic Mn moments triggers short-range order (for x = 0.1) and long-range order (for x ≥ 0.2) of the Tm³⁺ cations at the same temperature - an unusual situation in perovskite materials with a simple GdFeO₃-type Pnma structure. For x = 0.1, long-range IC magnetic order [with propagation vector k = (k₀, 0, 0) and k₀ ≈ 0.40] of Mn³⁺ and Mn⁴⁺ cations at the B site coexists with short-range order of Tm³⁺ and Mn²⁺ moments at the A site. Short-range order is induced at the Néel temperature T_N = 37 K, increases towards an additional specific heat anomaly at T = 4 K, and remains at lower temperature. The ferrimagnetic structure [with propagation vector k = (0, 0, 0)] consists of ferromagnetically ordered Mn³⁺ and Mn⁴⁺ cations at the B site which are coupled antiferromagnetically with ordered Mn²⁺ moments at the A site. Tm³⁺ moments adopt a zigzag magnetic structure which contains a macroscopic ferromagnetic moment that aligns with the direction of the ordered Mn²⁺ moments. Towards low temperature, the ordered Tm³⁺ moments strongly increase and overcome the saturated magnetic Mn moments at the B site, and this behavior results in the observation of magnetization reversal or negative magnetization phenomena with a compensation temperature of about 15 K at small magnetic fields in the x = 0.2 and 0.3 samples. This is a classical mechanism of the magnetization reversal effects for ferrimagnets.