There are two connections to make with the Wraith Prism, and one NOT to make.
First, its female 4-pin FAN connector must plug into your mobo's CPU_FAN header. Then you make a choice:
EITHER
(a) connect a cable with FOUR holes into a recessed 4-pin socket on the side of the cooler, and the other end of this goes to a mobo 4-pin (12 VDC) PLAIN RGB header IF you have one. If you have such a header, this way you can synchronize the Prism's display with your other plain RGB lights. If you use this method you do not need the special software for the Wraith Prism.
(b) INSTEAD of that, if you choose, or if you have no 4-pin plain RGB mobo header (this appears to be your case, OP) you do not use that cable. You use the other cable with THREE holes in one end, and plug it into the OTHER (3-pin) socket on the cooler side. The other end of that plugs into a mobo (10-1) pin USB2 header. Then you DO need to download and use the lighting control software utility.
Your post says you did Option (b). I hope you did NOT also connect the other cable for Option (a). Did you also make the connection to the CPU_FAN header? That is where the cooler gets its power for both the fan and the lights, AND where its fan speed is controlled, AND how the mobo can check that the fan actually is working (from the speed signal).