I just got my harmony this week and it definitely works to control a few smart things devices, not too many.
First, the current integration only works with harmony home. And not with harmony ultimate home. And not with any individual Harmony remote. But you can set it up so the Harmony Home remote talks to the harmony hub which talks to the Harmony cloud which talks to smart things cloud which talks to the smartthings hub which talks to a SmartThings connected device. Which is a long way around but does seem to work.
So, the first thing you have to do is tell your harmony account about your smart things account.
THE NATIVE HARMONY SETUP WIZARD 
I found the native harmony set up really horrible. It just didn’t work. I’m not talking the smartthings integration, I’m just talking setting up the harmony home.
I started it on the mobile app, but that didn’t work. There is a five step set up process clearly labeled as you go “step one of five,” “step two of five,” etc.
I switched to the desktop app. I was able to complete the steps one, two, and three, and start step four, but I was never able to complete step four so I could never get to step five.
So I completed steps one, two, and three, then skipped step four, and completed step five, all on the desktop.
Then I went back to the mobile app and did step four there.
Then I went back to the desktop, went into set up the hub, and chose the home automation tab. This was what let me tell Harmony about my smartthings account. Note that I did not do this through discovering smart things as a device.
Doing this from the desktop let me connect to my smart pthings account,and once there it worked just like ifttt, I authorized harmony to have access to smartthings, and I picked the individual devices that I wanted to allow harmony to control.
After that, I went back to the mobile app and assigned individual buttons on the remote to individual actions.
AVAILABLE HARMONY --> ST PROTOCOLS
I was able to do three different kinds of control protocols.
First, I set up the three “Harmony action buttons,” which are basically like scenes. They do let you combine devices of different Device classes, such as TV on and lights down.
Second, I was able to assign individual smartthings controlled devices to the “home automation buttons” on the remote, the ones which look like bulbs and outlets. This would probably be where you saw the groups information.
Finally, I used ifttt to give me some voice control over the Harmony actions, using the same method that will Poirier developed for voice control of smartthings.
So now I can press a “Home automation” button on the Harmony remote, and toggle a particular lamp on and off. I can press a “harmony action” button on the Harmony remote, and have quite a few different things happen. Or I can use Siri to send a #text message to IFTTT and trigger a “harmony action” that way.
THE HOME AUTOMATION TAB
So I suspect the first thing you need to do is find the set up home automation tab, which will probably be in the desktop harmony set up wizard. I assume there are other ways to get there, that’s just the one I used. There’s supposed to be a way to get there from the Harmony mobile app, but every time we tried the connection just hung forever. When we tried to get there from the desktop wizard it went pretty fast.
I would not assume that the same functionality is available in the desktop set up wizard and the mobile app set up wizard, because it is not. There are a lot of differences.
Good luck! I’m quite happy with Harmony as I have it now, because it did give me some voice control over the TV. Not much, but more than I had before. As far as using the remote to control smartthings devices, we do use a couple of the toggles a lot, but that’s about it.