Automated text annotation is a compelling use case for generative large language models (LLMs) in social media research. Recent work suggests that LLMs can achieve strong performance on annotation tasks; however, these studies evaluate LLMs on a small number of tasks and likely suffer from contamination due to a reliance on public benchmark datasets. Here, we test a human-centered framework for responsibly evaluating artificial intelligence tools used in automated annotation. We use GPT-4 to replicate 27 annotation tasks across 11 password-protected datasets from recently published computational social science articles in high-impact journals. For each task, we compare GPT-4 annotations against human-annotated ground-truth labels and against annotations from separate supervised classification models fine-tuned on human-generated labels. Although the quality of LLM labels is generally high, we find significant variation in LLM performance across tasks, even within datasets. Our findings underscore the importance of a human-centered workflow and careful evaluation standards: Automated annotations significantly diverge from human judgment in numerous scenarios, despite various optimization strategies such as prompt tuning. Grounding automated annotation in validation labels generated by humans is essential for responsible evaluation.