Please check the following:
- iCloud Sync is turned on in Roomie.
- iOS iCloud Settings has Documents and Data turned on.
- The iCloud Account configured in iOS iCloud Settings is the same on the two devices.
If 1-3 are true, activating an Activity on one device will reflect the same Activity on the other device within iCloud’s usual sync time which can be up to 30-60 seconds or so but is usually around 10 seconds. If the two devices are on the same Wi-Fi network, it should be on the fast side.