I've driven it manually, but I've also had it change to automatic without me asking it to. All I did to fix it was go into the options menu and check the auto shift. Didn't have to touch it, but just going into the options seemed to fix it.
I'm pretty sure the Camaro is supposed to be manual.
I'm not sure if this is a proper fix as such, or whether I just got lucky, but seems to work.