Humanoid robots require both robust lower-body locomotion and precise upper-body manipulation. While recent Reinforcement Learning (RL) approaches provide whole-body loco-manipulation policies, they lack precise manipulation with high DoF arms. In this paper, we propose decoupling upper-body control from locomotion, using inverse kinematics (IK) and motion retargeting for precise manipulation, while RL focuses on robust lower-body locomotion. We introduce PMP (Predictive Motion Priors), trained with Conditional Variational Autoencoder (CVAE) to effectively represent upper-body motions. The locomotion policy is trained conditioned on this upper-body motion representation, ensuring that the system remains robust with both manipulation and locomotion. We show that CVAE features are crucial for stability and robustness, and significantly outperforms RL-based whole-body control in precise manipulation. With precise upper-body motion and robust lower-body locomotion control, operators can remotely control the humanoid to walk around and explore different environments, while performing diverse manipulation tasks.