Update: A much simpler workaround than signing out of iMessage on additional devices. Someone else in the thread has mentioned bluetooth but I apologize that I do not know how to search within a thread to find their username and thank them.
The simpler, less disruptive workaround: Disable new bluetooth connections temporarily, or turn bluetooth off entirely, on either your phone or on all secondary devices in range. Your phone notifications will then work normally.
To temporarily bluetooth connections: in the Control Center, touch the bluetooth icon. When it changes from blue to white, new connections are disabled for 24 hours. To turn bluetooth off entirely, go to Settings > Bluetooth and toggle the bluetooth switch off. Alternatively in Control Center if Airplane Mode is enabled, the bluetooth button there will then function as an on/off. (It is ok to leave wifi on.)