Current Artificial Intelligence (AI)-based tutoring systems (AI tutors) are primarily evaluated based on the pedagogical quality of their feedback messages. While important, pedagogy alone is insufficient because it ignores a critical question: what do students actually do with the feedback they receive? We argue that AI tutor evaluation should be extended with a behavioral dimension grounded in student interaction data, which complements pedagogical assessment. We propose an evaluation framework and apply it to 10,235 code submissions with corresponding AI tutor feedback from an introductory undergraduate programming course to measure whether students act on tutor feedback and whether those actions are applied correctly. Using this framework to compare two deployed AI tutors across different semesters in a large-scale introductory computer science course reveals substantial differences in student engagement patterns that are not captured by pedagogy-only evaluation. Moreover, these engagement-based behavioral signals are more strongly associated with student perception of helpful feedback than pedagogical quality alone, providing a more complete and actionable picture of AI tutor performance.