Does voltage matter when using constant current PSU?
Yes, voltage matters. Just as a voltage source (as most power supplies are) have a maximum current and also a minimum current (usually assumed to be 0A, unless otherwise specified), a current source has a range of voltages over which it can work.

If required to work outside these ranges to supply the specified constant current, it may shut down, fail to supply the specified current, overheat, or spectacularly self-destruct.

I'm not sure what to make of the numbers you give. 26V-36V or 30V-36V doesn't make a lot of sense, because that's equivalent to just 26V-36V. Even so, if your red LEDs require 20V-22V, this is outside that range, which suggests this power supply will not work.

Furthermore, it sounds like you are thinking about driving multiple strings of LEDs in parallel with one supply. That won't work. Circuits in parallel have equal voltages. Circuits in series have equal currents. If you put multiple LEDs in parallel, and they don't each have some current regulation device (the simplest being a resistor), then the total current from the supply will be split between the parallel circuits. This is not what you want. See Why exactly can&#39;t a single resistor be used for many parallel LEDs?. Although that's about sharing a resistor, the question, and the answers, are just as applicable if you replace "resistor" with "constant current source".

Since your proposed LED modules are sold as a unit, we can probably assume they have some mechanism to equally share current among the internal parallel circuits. However, I see no datasheet, so we are taking it on faith. However, you will need a separate supply for each of those modules, or you can connect all the modules in series and find a current supply capable of supplying the sum of the voltages of each module.