There are 2 different approaches that you need to unpack.
Approach 1. Integration with Smartthings: Activities show up as switches. It would be the same as saying, “Alexa, turn on the light”…You are trying to say, “Alexa, Play the Kitchen Light”. She doesn’t understand those type of commands for Switches. Just on and off for the Harmony Activities. Now what you can do is create an Alexa Routine in the Alexa App: When I speak, “Alexa Play PS3” then Alexa turns on the related SmartThings Switch that is associated with the Harmony Activity. Play PS3 [Harmony Activity].
Approach 2. Leave SmartThings out of the equation altogether and do as @diademz suggested:
I use Approach 1 and have 4 Harmony Hubs. However, I am also heavily invested in the Amazon family of devices. I have an Echo and Fire TV for each Harmony Hub. So the integration is much more fluid.
Finally, if you go the ST route, which I highly recommend as you can actually integrate both approaches, then make sure you follow this tutorial to get instant updates when you start an Activity outside of ST.