They all seem to be using a simian adenovirus as a vector. The reason it's a simian rather than a human adenovirus is, as far as I understand, our pre-existing immunity to human adenoviruses, since we've been infected with them many times over the course of our lives. Whereas we have not been exposed to chimpanzee adenoviruses before, so our immune system is happily oblivious of their existence and will not attack them and prevent them from entering cells.
Fine. So does an injection of the vaccine count as an exposure of the immune system to this virus? Does the immune system learn about simian adenovirus antigens after a shot? Will it attack the virus itself during the second shot? What about the booster shot?