Tesla may have been working on it longer commercially, but Uber did poach a lot of expertise from Carnegie Mellon to get a head start:
http://www.businessinsider.com/uber-poached-a-load-of-staff-...
If Tesla is ahead, it's not by much. Uber is already demonstrating (alpha-testing?) self-driving cars in Pittsburgh.
https://techcrunch.com/2016/09/14/1386711/
I'm not sure why Uber needs to be directly working with a car company, other than for better integration of the self-driving technology with the vehicle systems. However, they are currently working with Volvo:
https://www.media.volvocars.com/global/en-gb/media/pressrele...