That splitter certainly will work for you. But there are two other issues you should think about.
1. General "rule of thumb" is that any mobo fan header can power two fans, but not more. So using three as you plan is risking POSSIBLE problems, although it may still work OK.
2. Those fans are 3-pin design, as far as I can tell. Look closely at them. Are there three wires coming out of the fan motor, and a connector on the end with 3 holes? If yes, you should know that you can only control the speed of 3-pin fans when they are plugged into a mobo port that is also a 3-pin design (Voltage Control Mode). Many mobos have both 3- and 4-pin CHA_FAN ports. SOME mobos with only 4-pin ports can be set in BIOS Setup to make those ports behave in true 3-pin (Voltage Control) Mode, rather than 4-pin (PWM Control) mode. If you connect 3-pin fans only to a 4-pin PWM Mode) port, the fans will run at full speed all the time.