The case information posted to mycase.in.gov is entered by the local courts that use the Odyssey case management system. As soon as a record is updated by the local court, that information is available on the site.
Any questions about updates to a case should be directed to the clerk's office in the county hearing the case. Phone numbers for all courts and clerks' offices across the state are available at https://www.in.gov/judiciary/files/court-directory.pdf