Containerization technology offers lightweight OS-level virtualization, and enables portability, reproducibility, and flexibility by packing applications with low performance overhead and low effort to maintain and scale them. Moreover, container orchestrators (e.g., Kubernetes) are widely used in the Cloud to manage large clusters running many containerized applications. However, scheduling policies that consider the performance nuances of containerized High Performance Computing (HPC) workloads have not been well-explored yet. This paper conducts fine-grained scheduling policies for containerized HPC workloads in Kubernetes clusters, focusing especially on partitioning each job into a suitable multi-container deployment according to the application profile. We implement our scheduling schemes on different layers of management (application and infrastructure), so that each component has its own focus and algorithms but still collaborates with others. Our results show that our fine-grained scheduling policies outperform baseline and baseline with CPU/memory affinity enabled policies, reducing the overall response time by 35% and 19%, respectively, and also improving the makespan by 34% and 11%, respectively. They also provide better usability and flexibility to specify HPC workloads than other comparable HPC Cloud frameworks, while providing better scheduling efficiency thanks to their multi-layered approach.