I posted this reply over on one of the other forums dealing with this same question so I thought I would repeat it here, but in the meantime I did some "work" on my phone...
I have an iPhone 5S running iOS 7.0.x (I think 3) on Verizon.
I have had, all the time, the background notifications that you speak of turned ON. I just went in and turned them both OFF, turned my phone OFF, turned my phone back on, re-turned on both the main and reminder settings, turned the phone off, then back on. ALL to the same result - nothing!
Here is what happens:
Go to Reminders App
Set a new reminder
to remind me at a location (arrive at home)
press "Details" and "Done" and it goes back to the Reminer home screen
When I FIRST get back to the Reminders home screen the "Arriving: Home" appears but within seconds (without ever leaving the Reminders app) that notation simply dissapears...
Do you have any further suggestions?
Thanks,
Keith