high-power LED voltage control?

You need to understand "constant current source". A constant current source will vary the voltage of its output to whatever value is necessary to keep the right current flowing. If you don't attach a load it will try to generate as high a voltage as possible, this does not reflect the behaviour with a proper load.

These constant current drivers are switching step-down regulators - all they need is a voltage in excess of the output voltage (by some margin), and they will efficiently convert the power to the output (93% according to the specs).

They say for 3 blue/green LEDs a supply of 15 to 24V will do, for red 12--24V will do. So you may find they won't drive the green/blue properly from just 12V.