>Do they have any models built-in onto the on-board processor or they access the models through API?
Foir the kind of cameras mentioned, MV12, they have a people detection model built into the camera. You have no access to the model. You can only retrieve a snapshot picture (or video clip) when it triggers.
>If the models are accessed through API, then if the internet connectivity is lost the cameras do nothing but recording the video.
The cameras keep recording if the Internet is lost. All processing is done on the camera. Typically if you are using the people detection you use MQTT, which is sent locally from the camera to an MQTT server that you operate.