Hills plus weight rule your engines RPM's until your transmissions clutches pick your gear. It is an open system, weight and hills will move your wheels forcing your engines rpm's up. Any part of an open system will and can effect every part of the system, IE what gear your tranny goes into or your gears spinning or RPMS spinning, etc.. Weight and hill will work just as pressing a gas pedal, will have a very similar effect on every part in your system. If any part of the system is closed, IE a manual transmission, the RPM's would just climb until something breaks or until you manually change the gear. Engine safe guards such as Governors are only mildly effective on hills. Any truck driver will tell you the governor wont keep you slow on hills, but will do great on flat surfaces. Hills and Weight rule.
So when you apply your brakes on a hill, it has the same effect as taking your foot off the pedal, because your are artificially changing the slope by slowing the weight. And when your rpm'***** the shift point, the transmission will kick down the RPM's right after the shift.