As expected, the answer is right there in your datasheet. Have a look at the schematic on page 8 (document page 5):
Do you see the "LED+" and "LED-" labels on the right hand side? Those correspond to the LED '+' and '-' terminals on the driver board. A constant current driver works by monitoring the feedback across a resistor, in this case "RSENSE," and changing the output voltage accordingly. You CAN connect multiple LEDs in series or parallel in between these leads, they would either share or split the output current. However, you CANNOT connect the negative terminal of one LED to one driver and its positive terminal to another driver. If you are using three drivers for an RGB LED, it CANNOT be common anode OR common cathode unless you want to put all three LEDs in parallel on the same driver, which would be pointless. You have to have three independent LED anodes and cathodes, one pair for each driver.
You CANNOT have a "shared ground" between your LEDS with this driver. You are confusing the LED ground (common cathode) with that of the power rail ground. They are NOT the same thing unless the LED is being driven some other way and its cathode is tied to the negative power rail.
Also, you mention in your question:
connect the positive output of the driver to the individual colors of
the led and the negative output to the shared negative connector of the led
which would imply common cathode (shared negative), not common anode (shared positive) as you mentioned in a later comment. It seems as though you have absolutely no idea what you are doing or talking about... which is OK, it just means you need to learn to research these things on your own. It's hard to help if you don't even know how to ask an appropriate question.