Like others have said, once you get the reminder, you have to stand up and walk around for a little bit.
It has always worked for me....I get the reminder, I stand up and just walk around the general area, then I get the notification that I've stood for a minute and I go sit back down.
You have to let your hands down to your side so it can detect that you're standing.
Also it will *only* remind you to stand if you've gone 50 minutes into the hour without standing. If you've stood at any point during the hour before the last 10 minutes, you won't get reminded. (but you should get credit for standing in the activity app)