^Correct. As I already stated, check your pads FIRST!
The pressure of the pedal is how the fluid pressure was setup. When your pads are almost gone and the fluid is short, the fluid level goes down because more fluid is needed to apply pressure on the piston. Thus causing the light to come on. The filter is a bobber thingy that floats in the reservoir. When the piston is pushed back in, via new pads, the fluid level goes back up. If you just fill it up and the pads are low, when you add new pads the tank will overflow. If you read the manual, it says to leave the cap off, when changing front pads, so that it can overflow if there is too much.