Thank you for contacting Syncfusion support.
Scheduler can be refreshed by using public refresh method, kindly refer the below link to know more about the function.
Note: On using refresh function, timezone difference will be added to an appointment duration and to overcome that kindly use applyTimeOffset property. Please visit the below link to know more about the property.
After dragging and dropping an appointment there is no need to refresh the Schedule, kindly share your code example/sample (if possible)/image/video demo of the issue so that we will analyze the cause for the issue.
Regards,
Karthigeyan