Here are my thoughts:

Hunter has been given the job of holding the 'Red Phone' which is a protected device where secret conversations can occur without being hacked and which show up with no caller ID or way to trace them back to the original caller. It may trigger a specific, urgent ring tone that will alert Obama immediately, whereas a regular call would not. The ringtone may tell Obama to go get in his SCIF to take the call where no one can listen in. This is clearly some sort of tech device set up between Obama, Joe and Hunter to carry out their clandestine actions.

Obama may have also instructed Joe not to call him at all as to maintain the appearance of a 'separation' between them.

Also, Joe is being surveilled all the time. He must have thought this call to his son was protected or safe. Maybe his Secret Service team (or other white hats) captured it and knew it needed to be heard.

Also, all kinds of eavesdropping devices are out there that you forget are listening to your conversations like your 'Smart TV,' Amazon Alexa and Apple phone's Siri, along with the usual suspects and foreign actors.