High-precision assembly frequently involves tight-tolerance insertions, where even slight pose errors can cause jamming or excessive interaction forces, making robust and safe insertion policies difficult to obtain. This paper proposes a tactile-augmented two-stage method that combines Imitation Learning (IL) and Reinforcement Learning (RL) for precision insertion tasks. In the first stage, IL learns a reaching policy with position generalization that grasps the peg and brings it to the vicinity of the target region. In the second stage, RL executes the insertion and enables recovery from failures during contact-rich interactions. To better exploit tactile feedback, we introduce tactile group sampling to increase coverage of critical contact segments during training, and design a tactile critic to more accurately evaluate policy values, improving insertion performance while maintaining low contact forces. We conduct systematic experiments across five hole geometries and three clearance settings. Results show that our method substantially improves insertion performance across all settings; under the most challenging 0.05\,mm clearance, it achieves a 67\% success rate while keeping contact forces low, reducing the maximum interaction force by 60\% and torque by 44\%, thereby validating both effectiveness and safety for precision assembly.

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