You don't say whether it's a 'side-by-side' or over-under... but regardless... there's only one source of cold air and that is first routed through the freezer section from the compressor.
Most likely, the thermostat you are setting not only regulates the amount of cold air in the freezer but opens a small 'door' between the freezer side and the fridge allowing cold air to enter. The small door is electronically controlled and opens and closes in response to 'cold' demand on the fridge side.
The noise you are heraing sounds like the new unit may have the capability of producing ice cubes. The sound may be the cycle the ice cube maker goes through even though you or the people who installed it for you didn't hook it up, which is often the case since they don't want to go to the trouble of routing a small water line to the firdge unless the owner specifically tells them to.
Or... your fridge may be an automatic defrost model and it's going through that cycle.
The cycle starts with the de-ice plate (in the freezer side, behind a panel) turning on for a short time. This plate actually heats up to melt the ice that's accumulated on it. The melted water from the plate runs donw a channel to the bottom of the freezer and drains into a holding panu underneath the outside of the fridege. Check your owners manual to see if you have this feature.
Additionally, if you do have the auto defrost feature, be sure to drain and clean the drip pan from underneath on a regular basis... it can grown mold and present a disagreeable odor that's hard to locate if you don't know about it...