If each user has their own phone, then they should only need to pair once at the beginning, after setting up their account for the first time.
When an additional user is setting up it is important for all other users to disconnect i.e. make sure the app is closed from the background on their phones. The device will disconnect from other phones after 10 mins if they are not being used anyway, but it is good practice to close the app completely if it is not in use.
If the Bluetooth icon is showing on the device it means it is connected to a phone and if you try to pair another phone when that is showing it won't allow it and the user will see an error message on the phone they are trying to pair.