No, you do not need to keep your smartphone on a 2.4 GHz network after you successfully set up your Roost device.
Roost Smart Devices need to be set up on 2.4 GHz networks as they only communicate with the Roost Cloud over this Wi-Fi band. So, during the setup of your devices, your smartphone needs to be connected to a 2.4 GHz network.
After your device is set up, it does not matter which Wi-Fi band your smartphone is connected to. Roost will send notifications of alarms to your smartphone whether your phone is connected to a 2.4 GHz Wi-Fi band, 5 GHz Wi-Fi band or a cellular network with data enabled.
The reason that your smartphone needs to be connected to a 2.4 GHz network during setup is because the Roost app takes the name (SSID) of your network from your smartphone. Together with your WI-Fi password that you input into the Roost app, the Roost app transmits this information via an encoded audio signal to the Roost device.
Once the Roost device is set up, that 2.4 GHz network name and password are stored in permanent memory on the device. This is how the device can access the Roost Cloud via your Wi-Fi router and the internet.
Questions? Please contact firstname.lastname@example.org.