Why do all the LEDs in this circuit light up at once?
Your LED array is common-cathode so you cannot use it with these PWM modules. This is inherent to the LED device itself and cannot be changed.
The PWM modules have the + in and + out more-or-less connected together (there's a polyfuse in each line) and that won't work for you.
You can use individual LEDs with resistors. It's also possible to use a common-anode RGB LED + resistors however the fuses will be paralleled, which is not ideal.
The module schematic (simplified) looks like this:



simulate this circuit &ndash; Schematic created using CircuitLab
LED array:



simulate this circuit