The JavaScript version exposes a set of events that let you handle the user input. Typically, the event handler will invoke a server-side endpoint using an ajax call.
These days, most Java frameworks make it really easy to create custom JSON-based web services API. And that's all you need on the server side - a couple of REST endpoints that load and update the data.
The Java version of DayPilot started back when most of the work was done on the server side. This has changed and now most people are comfortable with client-side development.
When you use the JavaScript client and custom server-side backend you get better control over what and when is being sent over the network. There is also no additional dependency on the server side.
You can also take a look at the following Scheduler tutorials:
https://code.daypilot.org/48990/machine-production-job-scheduling-web-application-spring-java
https://code.daypilot.org/70997/using-javascript-html5-scheduler-in-spring-boot-java
They show how to use the JavaScript version with a Spring backend. You can use the same approach with other frameworks as well.