The quantum anomalous Hall effect (QAHE) in a magnetic topological insulator system without the need of an external magnetic field becomes of great interest because of its dissipationless spin currents. The proximity effect via a magnetic adlayer is a promising strategy to bring magnetism into a topological insulator (TI) due to its boosted Curie temperature for a realistic application. In this work, a proximity-induced magnetism above 90 K in a TI, (Bi 0.25 Sb 0.75 ) 2 Te 3 , on a ferrimagnetic adlayer with perpendicular magnetic anisotropy, thulium-iron-garnet (TIG), was evidenced directly by using magnetic circular dichroism. A competition between exchange couplings with different sublattice-sites was further revealed element-specifically in a temperature-driven spin-reorientation of TI, bringing an issue on magnetic inhomogeneity at the interface, which might cause difficulties in obtaining QAHE in such a TI/TIG bilayer system. Our results prove directly the robust magnetism of TI above liquid nitrogen temperatures and also give a deep insight into the mechanism of interfacial coupling in the proximity effect for the bilayer of TI and magnetic oxide, which could be essential for the design of a system with QAHE.