Recent works have sought to enhance the controllability and precision of text-driven motion generation. Some approaches leverage large language models (LLMs) to produce more detailed texts, while others incorporate global 3D coordinate sequences as additional control signals. However, the former often introduces misaligned details and lacks explicit temporal cues, and the latter incurs significant computational cost when converting coordinates to standard motion representations. To address these issues, we propose FineXtrol, a novel control framework for efficient motion generation guided by temporally-aware, precise, and fine-grained textual control signals that describe specific body part movements over time. In support of this framework, we design a hierarchical contrastive learning module that encourages the text encoder to produce more discriminative embeddings for our novel control signals, thereby improving motion controllability. Quantitative results show that FineXtrol achieves strong performance in controllable motion generation, while qualitative analysis demonstrates its flexibility in directing specific body part movements. Code will be released.