I assume you figured this out by now, but it’s very easy.
Create a virtual switch to act as a proxy for the routine. Then have the Logitech activity turn that switch on.
In the routine itself using the set up wizard in the SmartThings mobile app, set the routine to run automatically when the switch comes on.
If you use the “momentary button tile” for your virtual device then The switch will automatically turn itself off again so it’s ready for the next usage. Otherwise, use smart lighting and set up the power allowance on the simulated switch so it will turn itself off.
Either way, the harmony activity tell smart things to turn on the virtual switch, the virtual switch comes on, the routine starts because the virtual switch came on. 
BTW, you can use the exact same virtual switch to start the routine via echo, Google home, another smart app – – anything which can turn on a switch in smartthings.