After a new device is paired to an iPhone, if you wish to use it for hands free calling the user must select the Bluetooth device for hands free calls. The user can do this while on a phone call.
After you have answered a phone call, make sure the desired device is paired to the iPhone via Bluetooth.
Once the call is answered, the call options should appear. Click the Audio Source option, then on the second screen, select which device to use for hands free calling.
On an Android device, you may need to manually select the Bluetooth for calls as well. A screen shot below shows the call screen on an Android phone. Make sure that "headset" is selected while on a phone call.