You are in luck. First, true 4-pin fan headers that actually use PWM Mode for control can control 4-pin fans, but not 3-pin ones. And my guess is that your case came with pre-installed 3- pin fans.
Now the good news. Your mobo uses a 4-pin header, BUT the pin labels showing on p. 13 of the manual indicate that its SYS_FAN header is NOT using PWM Mode - it is using the older Voltage Control Mode. That method WILL work with both 3-pin ad 4-pin fans. This is exactly why many mobo makers today use this system of a 3-pin fan control system on a 4-pin header - so people like you with pre-installed 3-pin fans do not have a problem.
Now, as to a Splitter, it does not matter whether you buy a 3-pin or a 4-pin Splitter. Both will work with...