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Teacher simulations increasingly incorporate generative AI agents to mimic students, yet the impact of AI architectures on human-teacher feedback remains underexplored. Analyzing 251 conversation sessions with 1,618 coded dialogue turns across GPT and rule-based conditions, this study employed sequential data analytics, including pattern mining, Markov modeling, and lag sequential analysis. Findings indicate GPT agents elicit more diverse student responses, such as emotional expressions (S:EE → T:Q, 0.672 probability) and complex multi-turn patterns (30 unique). Conversely, rule-based agents foster structured questioning (T:Q → S:R, 28.3%) and sustained inquiry (29 patterns). Student difficulty expressions (S:ED) prompt scaffolded responses predictably (GPT: 0.701; Rule: 0.873). Teacher querying persists across lags (Lag-2: 47.9%), while directives signal termination.