Just writing this for people that run into the same issue as it confused me. I don't own an iOS device but wanted to purchase some algorithms and borrowed my friend's iPad. I synced a few presets from the various algorithms to my H9 pedal and figured I would be good w/o the iPad and returned it.
When connecting via USB and firing up the H9 control app on my mac, I was surprised to not see the algorithms I had purchased. The trick is to go into settings, restore purchases. This will transfer the purchased algorithms that are stored in the pedal into the OSX app and then you'll have full access to all the presets and full editing capabilities.