During instruction fine-tuning (IFT), large language models (LLMs) learn to follow instructions by using the provided context to answer a query. While prior work has studied how context characteristics correlate with context usage by the LLM, this analysis has been limited to inference time, leaving open how these relationships are acquired in the first place. Here, we measure how models' sensitivity to such characteristics shifts across successive IFT stages: supervised fine-tuning (SFT), direct preference optimization (DPO), and reinforcement learning with verifiable rewards (RLVR). Experiments across four models and three datasets show that SFT makes models more likely to use contexts that are easy to understand, such as containing high length, context-query similarity, and fluency. Post-SFT dynamics may either reinforce or resolve these preferences depending on the training dataset. Our findings reveal that context usage is actively reshaped at each IFT stage, and designing a balanced IFT dataset is important in ensuring robust context utilization of instruction-tuned models.