I guess that you saw the car in front's boot rise up as it braked heavily, and you reacted to that, while the Tesla doesn't react to that, so needed another half second to see the deceleration, which it actually had plenty of time for. It was probably in full control of things, nothing particularly unusual was happening. When taking over control, it is inevitable that you will not get things perfect, you were not ready.
In the end, it was the lady behind following too closely that caused the accident, and she is at fault under law, but the unusual thing was you stopping suddenly with a significant gap to the person in front. Having two things in charge of the controls is never going to work well, either the car should have full control, or the driver should have full control, not both. At some point, the car will be the better driver and should be trusted.