Emotion Recognition in Conversation (ERC) focuses on identifying static emotional states, overlooking the cognitive mechanisms that drive emotional transitions. This work introduces a novel emotion prediction task grounded in Appraisal Theory, which conceptualizes emotion as a cognitive evaluation of expectations and their violations. To address this task, we develop a prompt-based reasoning framework that breaks emotional dynamics into three interpretable stages, e.g., expectation inference, violation detection, and emotion-shift prediction, thereby explaining not only which emotion is expressed, but also why it emerges. To examine whether LLMs exhibit human-like affective reasoning, we design six appraisal-informed prompting tasks and evaluate eight representative LLMs across four conversational corpora. A unified two-level evaluation, which measures both emotion classification and transition dynamics, reveals that explicit expectation cues improve accuracy by up to +2.4%, whereas violation-only cues often degrade performance. Our analysis uncovers a robust appraisal pattern across models and datasets: expectation construction is the primary contributor to accurate emotion prediction, while isolated violation cues tend to induce misattribution rather than improve causal reasoning. Beyond label accuracy, transition-level evaluation shows that LLMs capture emotion-shift direction above chance but exhibit a marked stability bias, over-predicting no-change trajectories and under-detecting fine-grained shifts. These findings demonstrate both the promise and the current limits of LLMs in appraisal-driven affective reasoning, and motivate a new cognitively-grounded research direction.