Due to the increasing use of service chatbots in E-commerce platforms in recent years, customer satisfaction prediction (CSP) is gaining more and more attention. CSP is dedicated to evaluating subjective customer satisfaction in conversational service and thus helps improve customer service experience. However, previous methods focus on modeling customer-chatbot interaction across different turns, which are hard to represent the important dynamic satisfaction states throughout the customer journey. In this work, we investigate the problem of satisfaction states tracking and its effects on CSP in E-commerce service chatbots. To this end, we propose a dialogue-level classification model named DialogueCSP to track satisfaction states for CSP. In particular, we explore a novel two-step interaction module to represent the dynamic satisfaction states at each turn. In order to capture dialogue-level satisfaction states for CSP, we further introduce dialogue-aware attentions to integrate historical informative cues into the interaction module. To evaluate the proposed approach, we also build a Chinese E-commerce dataset for CSP. Experiment results demonstrate that our model significantly outperforms multiple baselines, illustrating the benefits of satisfaction states tracking on CSP.