Postman, utilizing Docker since early 2017, adopted a centralized and standardized approach for their microservices architecture to improve operational flexibility and reduce overhead in deployments. Their strategy involves using a common base image for all applications, facilitating a seamless integration of code through CI processes, and ensuring zero downtime during deployments. The document emphasizes the importance of starting with Docker to unlock long-term value and suggests keeping individual Docker files in source code while enhancing security and logging configurations gradually.