The appearance of an alternate case in a scheduling app after being notified and re-syncing the app will depend on the app's technology. Modern apps generally update in real-time or near real-time, but you should confirm with the app's support for specific operations and in case of technical issues.
The question appears to address the functionality of a scheduling application, likely related to a particular service or job field, rather than any specific academic subject. If you are notified on the same day that you have an alternate case scheduled, whether or not the new case will automatically appear on your app upon re-syncing will largely depend on the app's design and the efficiency of the scheduling system in use. In most cases, modern scheduling apps should update in real-time or near real-time, and a manual re-sync should ensure that the latest information is displayed, including any new client appointments or changes.
However, this process may vary depending on the specific app and the technologies involved. It's important to check with the app's support or technical documentation, or the scheduling team, for confirmation of how the system operates. If the app's syncing functionality is robust, you should see the new case appear promptly after the update. But technical issues can always arise, so it's wise to verify success after syncing.