Ahh, don't be so scared of electronics. It's not all smoke and mirrors. DC Power supplies are not as consistent to output as one thinks. Like your 12v battery in your car is 10-14v, in reality a power supply will often vary from the label in actual output.
The controller will have 2 things inside. 1 - Something to convert the 24v DC to whatever voltage the microprocessor is running on. I'd guess 5v, but could be anything really. New power circuits accept a wide voltage input (like a buck converter) and convert to the correct output or if a really dumb circuit (resistors) will just make less power then the controller needs as the voltage out has a relationship to voltage in. Under voltage in, under voltage out. If there isn't enough voltage controller or LEDs will not power on, like a dead battery still makes electricity, just not enough.
2 - The controller will regulate the input to the motors via some motor control method. Its modulating the power (on/off quickly) so the motor will see 19v vs. 24v through this control circuit. This will cause the motor to spin slower. Not a big deal either, it will just never reach the 24v speeds which it about a 20% Hit to the speed if linear. You could control a DC motor with voltage in vs modulation, but the circuit needed to do that is much bigger (old tech) and not very controller friendly.
There are some electronics that are very voltage sensitive, but those are typically old (predigital stuff) or measuring devises, etc. Pumps are pretty stupid so you just don't want to supply more power then they are designed for. Less is ok, it will just not perform as well.