They are not compatible.

On the LED strip side, the three together red green white is the control, Red = Positive, White = Common/Negative, Green = Data

The separate Red White is for power injection if you are chaining multiple sets of LEDs together.

Your controller is not designed for WS2812B LEDs If you want to use that controller you would want something like this: https://www.amazon.com/gp/product/B07G48K7C1

So the tape you linked is addressable tape, so each LED has it's own dimmer and control circuit. The four connections it uses are a DC voltage + and -, and then a data input. The integrated circuits and dimmers decode the data signal and then vary the voltage going to the LED's.

The decoder you link is for up to four channel tape, e.g. RGBW tape, where the whole length of the tape is controlled together.

Depending on which way you want it, you would use either a controller which takes in dmx/artnet/sACN and outputs a ws2812 data signal, or use tape which is non-addressable and has whatever colour profile you're happy with. Depends what you want to do with the tape.

If you don't mind building You could make some DMX controllable LED strips:

LEDs: https://www.amazon.com/BTF-LIGHTING-2700K-3000K-Colors-Multi-Colored-Non-Waterproof/dp/B07G48K7C1

C channel: https://www.amazon.com/dp/B07RBB1XJP

Controller: https://www.amazon.com/dp/B07Q1ZJZN9

Power Supply: https://www.amazon.com/dp/B07D9FTC77

Like $140 for 16ft of LED wall wash lighting,

I have STL file for a mount to join the controller and Power Supply together if you have a 3d printer.

If you don't mind more involved building, you can make bigger LED light bars, We use 1 by 2 wood, and luan to build 3 inch wide, 2 inch deep, C channels then cut up flat Fluorescent Light Fixture Covers as the diffusers. worked great and cheep.

Example of them in use: https://imgur.com/BmuvbRp