As explained in Barnes Univ.; if you are throwing loads over 60 or so grains you will get a more efficient powder burn with a magnum primer, therefore more velocity because you burned more powder in the cartridge case.
Put another way; The more powder you can burn in the cartridge case the more gas pressure will be created and the more velocity you will generate.
This is why WSM cartridges generate the same velocities with 12% less powder.
The powder is strung out the length of the cartridge case as it lays parallel to the earth (like on a shooting bench). The longer the "line" of powder, the longer it takes to burn. Once the gas pressure is sufficient to pop the bullet out of the crimp, the burn rate of the remaining powder drops big time. There are some interesting test result on the web showing this relationship.
Take a 300 WSM
cartridge and a 300 win mag cartridge and lay them on a table. Its easy to understand that the powder in the 300WM would take longer to burn than a 300WSM due to the length of the "line" of powder, even though we are talking mili sec.