How reminders work
Reminders are scheduled on your device and re-checked every time you open the app.
The app computes which reminders you should have, compares that with what your device has scheduled, and adds or cancels the difference. Logging, snoozing, skipping, or changing a plan re-checks immediately.
Lock-screen text is discreet by default. You can choose to show the person or full details after reading what that reveals.
The Notification health screen shows permission state, the last check, the next reminder, and platform-specific limits. It never says reminders are guaranteed, because operating systems can delay or drop them.