That's evolution, we don't do calendar event notifications ourselves.

Thanks for a bug report. That is correct and expected behaviour. Every software gives you past notifications for the time since you last opened it. It gives you an overview of possibly missed events. I agree it can be confusing with collaborative servers, where more clients (and eventually devices) access it, thus you get the notification in other applications, but it's still correct, especially when the server doesn't have a common mechanism to mark the reminder as already processed, understood by each singe application accessing the server.

My personal feeling is that these notifications shouldn't be shown. I haven't had a single instance when they've been useful, and they have always felt unwelcome.

Different people use it differently. There is a request where a user wants to keep the list of the notifications until explicitly dismissed, surviving restarts. It's the exact opposite of your request, which leads me to an idea to give an option for this, like:
  [x] Remind about past events
checked by default, shown in Edit->Preferences->Calendar and Tasks->Reminders tab.

Would that work for you?

I'm not a fan of millions of the options, but there are cases where one way doesn't work for everybody, like here.

Would it be on or off by default?

On by default, to keep backward compatibility.

(In reply to Milan Crha from comment #4)
> Different people use it differently.

In which case is this useful? I can understand notifying the last appointment, or an on-going appointment, but this is a major problem when I start a computer after a couple of weeks, or months.

Note that these are appointments, not reminders for tasks (which I could understand).

See also:
https://bugzilla.gnome.org/show_bug.cgi?id=719739

Another piece of anecdotal evidence:
I asked Fabiana if she uses the gnome integration with google calendar to get reminded about work meetings, but she said she disabled calendar notifications all together, since it keep spamming her about past meetings.

I added Edit->Preferences->Calendar and Tasks->[ ] Display reminders for past events, off by default. Despite the name, it covers also tasks and memos (the name with "events, tasks and memos" looked weird. It doesn't apply to snoozed reminders.

Created commit e4d4776 in evo master (3.23.90+)

Hrm, no, it doesn't work properly. It requires more changes than the above.

Created commit 93ee068 in evo master (3.23.90+)