while in QGIS, zone 12S appears to be in the southern hemisphere. Probably a ridiculous question, but not quite sure what am I missing.
There are 60 UTM Zones, each 6 degrees wide (about 700km at the equator), and stretching from 84 degrees North to 80 degrees South (the poles are reference with the Universal Polar Stereographic grid system). So the "UTM Zone" is technically just the number part (eg: 12), a long strip effectively from pole to pole, within which Eastings and Northings are defined in meters. The Northings are specified as either north or south of the Equator... in the north, the equator is zero meters. In the south, the equator is 10,000,000m.
Each zone is divided into "Latitude Bands", denoted by the letters shown in Google Earth. These are technically not part of UTM, but part of the closely related Military Grid Reference System (MGRS).
It looks like QGIS is showing you the N (north) and S (south) parts of Zone 12, while Google Earth is showing the "Band S" in Zone 12.
You can find a lot more information about the UTM grid system at these links:
QGIS is using the EPSG registry http://www.epsg-registry.org/ as the authority and in the EPSG registry the Area of Use for EPSG:32712 is between 114°W and 108°W, southern hemisphere between 80°S and equator, onshore and offshore.
The northen part has another EPSG code, EPSG:32612, and it is valid between 114°W and 108°W, northern hemisphere between equator and 84°N, onshore and offshore. Canada - Alberta; Northwest Territories (NWT); Nunavut; Saskatchewan. Mexico. United States (USA).