If your wiring is good (i.e. not shorted), you must see the same current at the magnets as at the brake controller. The electrons don't have anywhere else to go; current into a wire equals current out of said wire.
And yes, thanks to Ohm's law, it is impossible to have voltage and current controlled independently of each other for a resistive load. The laws of electromagnetism are most directly stated in terms of current, so the brake controller is eventually controlling the average current...but the average voltage has to likewise vary. Measuring the voltage at the controller and at the brakes would tell you what the voltage drop is between them, a very useful thing to check.
Do make sure that the ground return path is properly functional too.
