As Differential Privacy (DP) transitions from theory to practice, visualization has surfaced as a catalyst in promoting acceptance and usage. Despite the potential of visualization tools to support differential privacy implementation, their development is limited by a lack of understanding of the overall deployment process, practitioner challenges, and the role of visual tools in real-world deployments. To narrow this gap, we interviewed 18 professionals from various backgrounds who regularly engage with differential privacy in their work. Our objectives were to understand the differential privacy implementation process and associated challenges; explore the actors (individuals involved in differential privacy implementation), how they use or struggle to use visualization; and identify the benefits and challenges of using visualization in the implementation process. Our results delineate the differential privacy implementation process into five distinct stages and highlight the main actors alongside the diverse visualization applications and shortcomings. We find that visualizations can be used to build foundational differential privacy knowledge, describe implementation parameters, and evaluate private outputs. However, the visualization strategies described often fail to address the diverse technical backgrounds and varied privacy and accuracy concerns of users, hindering effective communication between the different actors involved in the implementation process. From our findings, we propose three research directions: visualizations for setting and evaluating noise addition, evaluation of uncertainty visualization related to trust in differential privacy, and research focused on pedagogical visualizations for complex data science topics.