The turbo is spinning whenever the engine is running, even when it isn't providing any boost. It always has exhaust gas going through it.For some reason, I believe it has to do with the torque converter in the autos, the manual models do not get their full boost and torque until 2,500 RPMS rather than the auto's 1850 RPMS.
Note: Here is the specs of the auto vs manual. (Look under torque for the 1.4L)
Chevrolet Pressroom - United States - Cruze
The manual has a different tune, that keeps the waste gate from fully closing, until 2500 rpm. This prevents excessive cylinder pressure at low RPM. An auto will never be able to run at full load at 1850 RPM, so the tune can be a bit more aggressive.