Yes, clamping too tightly can potentially risk damaging a carbon frame. The clamp needs to grip just snug, but not too hard.
Most roof rack clamps are highly adjustable to cater for all widths of frames. I'm afraid I've got a Thule so it might not be directly relevant but on those it's easy to do by rotating the locking handle to the right width before you close it off, exactly as you would with a QR skewer on your wheels. I'd imagine the Cruz has something similar. Like Figbat says, the clamp is really there to stop lateral movement of the upright frame, it's the wheel tethers that hold the bike to the roof.