The solution is to use Spring Cloud Bus to propagate the configuration change to multiple instances over a message broker such as RabbitMQ.
The following figure shows how different instances of a microservice (actually, they can be completely different microservices as well) are connected to a message broker using Spring Cloud Bus:
Each microservice instance will register with the Spring Cloud Bus at application startup.
When refresh is called on one of the microservice instances, Spring Cloud Bus will propagate a change event to all the microservice instances. The microservice instances will request the updated configuration from the configuration server on receiving the change event.