Large Language Models (LLMs) are increasingly used for automated unit test generation. However, it remains unclear whether these tests reflect genuine reasoning about program behavior or simply reproduce superficial patterns learned during training. If the latter dominates, LLM-generated tests may exhibit weaknesses such as reduced coverage, missed regressions, and undetected faults. Understanding how LLMs generate tests and how those tests respond to code evolution is therefore essential. We present a large-scale empirical study of LLM-based test generation under program changes. Using an automated mutation-driven framework, we analyze how generated tests react to semantic-altering changes (SAC) and semantic-preserving changes (SPC) across eight LLMs and 22,374 program variants. LLMs achieve strong baseline results, reaching 79% line coverage and 76% branch coverage with fully passing test suites on the original programs. However, performance degrades as programs evolve. Under SACs, the pass rate of newly generated tests drops to 66%, and branch coverage declines to 60%. More than 99% of failing SAC tests pass on the original program while executing the modified region, indicating residual alignment with the original behavior rather than adaptation to updated semantics. Performance also declines under SPCs despite unchanged functionality: pass rates fall to 79% and branch coverage to 69%. Although SPC edits preserve semantics, they often introduce larger syntactic changes, leading to instability in generated test suites. Models generate more new tests while discarding many baseline tests, suggesting sensitivity to lexical changes rather than true semantic impact. Overall, our results indicate that current LLM-based test generation relies heavily on surface-level cues and struggles to maintain regression awareness as programs evolve.