Recent advancements in Retrieval-Augmented Language Models (RALMs) have demonstrated their efficacy in knowledge-intensive tasks. However, existing evaluation benchmarks often assume a single optimal approach to leveraging retrieved information, failing to account for varying user needs. This paper introduces a novel evaluation framework that systematically assesses RALMs under three user need cases-Context-Exclusive, Context-First, and Memory-First-across three distinct context settings: Context Matching, Knowledge Conflict, and Information Irrelevant. By varying both user instructions and the nature of retrieved information, our approach captures the complexities of real-world applications where models must adapt to diverse user requirements. Through extensive experiments on multiple QA datasets, including HotpotQA, DisentQA, and our newly constructed synthetic URAQ dataset, we find that restricting memory usage improves robustness in adversarial retrieval conditions but decreases peak performance with ideal retrieval results and model family dominates behavioral differences. Our findings highlight the necessity of user-centric evaluations in the development of retrieval-augmented systems and provide insights into optimizing model performance across varied retrieval contexts. We will release our code and URAQ dataset upon acceptance of the paper.