Like most repeaters, the car transmits on frequency and listens on a different frequency. The repeater listens on the frequency that the car transmits on and retransmits on the repeater's output frequency. Generally, it's best to listen to the repeater's output frequency and trunked systems are no different in this regard.
Since this is a trunked system, when a user presses their PTT, they request a frequency pair to talk on their selected talkgroup. The site controller then says "all stations tuned to this talkgroup, go to this pair". The pair will be one of the voice channels listed for that site. This all happens in microseconds and the user has no idea its happening.