Here is one of the latest videos of the Tesla Autopilot view from the main camera, shared by greentheonly, in which a Tesla follows a fire truck in the city.
As you can see, the on-board computer analyzes the image from cameras (and other sensors) and then adds layers of identified stuff like vehicles, people (each with its ID, position and speed) and lines.
Autopilot needs to deal with tons of things happening at once, even the fire truck, which turns left with the right blinker on.
This is clearly a very difficult situation for Autopilot due to congestion and numerous activities and movements sensed. It really is quite amazing to see what the system sees and digests though.
From the video description:
this is a boring video that shows Tesla does see firetrucks.
at 3:16 we have the truck leaving our lane completely and that's when it's no longer seen as obstacle (the start next to id at the top)