Single-Source Personalized PageRank (SSPPR) is a fundamental problem in social network analytics, yet maintaining accurate SSPPR query results in evolving social networks poses significant challenges, especially for real-time applications. Existing approaches often overlook the role of subgraphs and struggle with frequent graph updates, resulting in inefficiency regarding dynamic scenarios. In this study, we define a novel personalized PageRank query, n-steps SSPPR, designed to address the challenges of dynamic environments. To support this query, we propose a baseline solution, Pn-FORA, as a foundational approach. While effective, Pn-FORA is inefficient due to its computationally expensive information update scheme. To overcome these limitations, we propose a multithreaded framework for processing massive-scale n-steps SSPPR queries in real-time over evolving graphs. Central to our framework is the Global Walk Synchronization (GWS) method, ensuring the accuracy of SSPPR scores by synchronizing walk information across nodes as the graph evolves. To further enhance GWS, we introduce an influence-aware graph representation to optimize update propagation. Furthermore, we develop a dynamic workload balancing strategy and precision-aware concurrency controls, which achieve an effective balance between efficiency and accuracy. Extensive experiments on real-world datasets demonstrate that our approach significantly outperforms existing methods, offering superior scalability and efficiency for real-time n-steps SSPPR query processing over large-scale social networks. The source code of our implementation is publicly available at https://github.com/SujunShuai/Work2023.