Commits won’t appear immediately since synchronization is implemented as background job (GitRevisionIndexerJob). You can reduce the job delay down to 1 minute to schedule updates more often.
Navigate to the General settings of the Git Integration for Jira app.
Scroll down to the Scheduled jobs section and set the Repository indexing value or leave it as is (recommended).
For near-instantaneous display of commits in your Jira issues, we recommend to configure webhooks.