This work reports the ferromagnetism of topological insulator, (Bi,Sb)₂Te₃ (BST), with a Curie temperature of approximately 120 K induced by magnetic proximity effect (MPE) of an antiferromagnetic CrSe. The MPE was shown to be highly dependent on the stacking order of the heterostructure, as well as the interface symmetry: Growing CrSe on top of BST results in induced ferromagnetism, while growing BST on CrSe yielded no evidence of an MPE. Cr-termination in the former case leads to double-exchange interactions between Cr³⁺ surface states and Cr²⁺ bulk states. This Cr³⁺-Cr²⁺ exchange stabilizes the ferromagnetic order localized at the interface and magnetically polarizes the BST Sb band. In contrast, Se-termination at the CrSe/BST interface yields no detectable MPE. These results directly confirm the MPE in BST films and provide critical insights into the sensitivity of the surface state.