Roomie 1.6 introduced Activity Memory. If you turn on “iCloud Synchronization” in Settings, the Activity Memory feature is then turned on as part of that.
This provides exactly the feature you’re talking about where starting an Activity on one device should reflect on all of your other devices running Roomie (assuming they are on the same Apple ID with iCloud Synchronization turned on).
Note that Activity Memory has no relation to whether a given target device supports multiple connections as you point out. That’s something that needs to be accounted for in the system design by making sure to use iTach units for instance instead of GC-100 units for IR, etc.