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Instruction tuning is commonly assumed to endow language models with a domain-general ability to follow instructions, yet the underlying mechanism remains poorly understood. Does instruction-following rely on a universal mechanism or compositional skill deployment? We investigate this through diagnostic probing across nine diverse tasks in three instruction-tuned models. Our analysis provides converging evidence against a universal mechanism. First, general probes trained across all tasks consistently underperform task-specific specialists, indicating limited representational sharing. Second, cross-task transfer is weak and clustered by skill similarity. Third, causal ablation reveals sparse asymmetric dependencies rather than shared representations. Tasks also stratify by complexity across layers, with structural constraints emerging early and semantic tasks emerging late. Finally, temporal analysis shows constraint satisfaction operates as dynamic monitoring during generation rather than pre-generation planning. These findings indicate that instruction-following is better characterized as skillful coordination of diverse linguistic capabilities rather than deployment of a single abstract constraint-checking process.