Both cams have control, yes. Theres a constantly variable situation for either cam. Typically intake cam is advanced on acceleration and the exhaust cam is retarded on cruising(to create an egr effect). But throttle input will change the degree of which cam is advanced or retarded under a huge range. You can't think of it in an "on/off" scenario.
I've not watched datalogs on cold start but i believe both cams are retarded on cold start so the pcm can command higher throttle input to load the engine in order to get the catalytic converter hot. Notice how much louder the exhaust note is on a cold start idle.