Well, the specifications of the device you linked are grossly inadequate.... but given you have 10 LEDs in series, I expect you'll operate at something like 40VDC...
Arduino analogWrite function generates PWM at about 490Hz.
I would suggest setting up a high side switch with a P-channel MOSFET (e.g. IRF9Z24) conrolled by an NPN BJT (e.g. 2N3904). Say 100ohm resistor into the base of the BJT and a 4.7kohm pullup on the gate of the MOSFET. Connect LED between MOSFET drain and GND. Connect PWM input to the aforementioned 100 ohm resistor.
If a module has only two terminals, but has some parallel LEDs internally, you can probably assume there's something inside the module to balance the current between each parallel circuit. This is made somewhat easier when all the LEDs are in one module because they can share a heatsink, and thus the temperature of each is likely close, and temperature variations are a big factor in why parallel LEDs will not share current equally. Each LED was also likely manufactured at the same time, so have very similar characteristics, which you can't guarantee when taking discrete LEDs out of a jar. The module may also include some small resistance in each parallel circuit to help balance. Point being: assume the manufacturer has taken care of this, and all you need to worry about is supplying the correct current to the two terminals provided by the module.
Your particular module is really like three modules, one for each color. It looks like there is one common terminal on the bottom, and three separate terminals on the top, one for each color. I can't find a datasheet that specifies if the cathodes or the anodes are common, so you may have to figure it out for yourself. It looks like maybe you can cut the common terminal apart if you want, but again, I see no datasheet, so you might have to experiment for yourself.
There is no special kind of LED driver that can drive parallel LED circuits. If an LED driver's job is to pump electrons, there's no way for it to tell some electrons to go down one circuit while telling others to go another way. The electrons decide which way to go by going whichever way minimizes their potential.
So, what you want to do with this module is power each of the R, G, and B sub-modules with a suitable driver (or if you can find it, one box that actually has three drivers in it). What you don't want to do is try to put the R, G, and B sub-modules in parallel and drive them all together. Since each color has a different forward voltage, this won't even remotely work: the color with the lowest forward voltage (red) will take very nearly all the current and all the power, and possibly be destroyed. At best you just won't get the other colors to light.
Best Answer
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'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.