Gmail – After making a notification in calendar I received an email but I did not get the pop-up

Now you can set when you will be notified for All-day events in the Google Calendar Settings.

1. Go to calendar.google.com in your browser
2. Click on the gear icon in the upper right and choose Settings
3. Choose Calendars from the top menu
4. Select 'Edit notifications' for the calendar you wish to edit this setting for. The first calendar listed will be your primary calendar, and usually the one you'll want to work with
5. The second setting All-day event notifications allows you to how many days before and at what time you wish to receive the notification
6. Be sure to click Save before leaving this page

That's an unusual calendar strategy.

Reminders work by sending an alert (email, popup, SMS) at X minutes/hours/days/weeks before the start time of the event.

You can set multiple reminders for an event, so you could do something like have a reminder sent three hours prior, then two hours prior, then an hour, then fifteen minutes. (If that's something you want to do.)

So, for your 12:00 appointment, you would create the actual event at 12:00. To receive a reminder at the time the event starts, create a reminder for 0 minutes "before" the event. If you want a reminder sent at 7:00, just create a reminder for 5 hours before the event.

Having a reminder sent after the event is to have taken place would seem to make no sense and it's no wonder to me that that's not how it's implemented. (For what it's worth, I've never seen any other calendar app implement reminders after the fact.)

Perhaps if you edit your question to explain why you're trying to do what you're doing, we might be able to offer a more viable strategy.