This device is what I prefer to call a HUB, although the maker (and many others) use the term Splitter. To me, the difference is that a Splitter can only supply power to its fans from the mobo header, connecting them all in parallel. A HUB, as I use the term, can share most of the mobo header's signals to all its fans, but most importantly gets all of the POWER for its fans from the PSU directly. THAT is what this device does. So YES, you must connect the device's wide connector to a 4-pin Molex female power output connector from the PSU to provide the power for the fans. The smaller 4-pin female (with holes) connector goes to a mobo SYS_FAN header to make connections. Then each of your fans plugs into one of the male (with pins) output connectors, making sure that one of those fans connects to the single output that has ALL FOUR wires coming to it.
Four-pin fans work this way. On the mobo header with 4 pins sticking up, there is a plastic "tongue" sticking up beside Pins 1 - 3, and Pin #4 is alone at the end. Pin #1 is Ground, #2 is always a full +12 VDC, Pin #3 carries the speed signal, and Pin #4 has the special PWM signal. So Pins 1 and 2 supply the power connection for a fan motor. The speed signal is a series of pulses (2 per revolution) generated inside the motor and sent back to the mobo header on Pin #3 for counting so you can "see" the speed. Inside the motor there is a small chip that uses the PWM signal from Pin #4 to modify the flow of current from the +12 VDC supply through the motor, reducing its speed to what the PWM signal requires.
A normal mobo fan header can supply from Pin#2 up to 1.0 A current for all fans connected to it. Many common fans (not the ones that have LED's) consume about 0.10 to 0.25 A, so you can connect a small number of these to a single header by using a simple Splitter. That is my term for the device that simply connects all its fans in parallel to the mobo header, so that all fan power must come from that source. But if your group of fans needs more that 1.0 A, you need to use a HUB instead, and that is what your device is. It makes most of those same connections between the mobo header and all its fans, BUT not for the +12 VDC power supply. For that, the Hub gets the power from the PSU directly via that extra cable that plugs into a Molex PSU output. This can supply MUCH more than 1.0 A, so you can connect many fans this way.
To use such a 4-pin fan Hub, though, requires two things. First, the fans used ALL must be of the 4-pin design that knows how to use the PWM signal to control its own speed. Three-pin fans are controlled differently and lack the special chip that can use the PWM signal, so they cannot be used with this type of Hub. Likewise, the Hub system depends on having a PWM signal, obtained from Pin #4 of the mobo header, to pass on to all its fans to share. Now that CAN get slightly complicated. These days virtually all mobo fan headers have 4 pins, BUT they do NOT all guarantee to be using PWM Mode to control fans, so you cannot tell from pin count alone whether the header does supply the PWM signal your Hub will need for its fans. IF you want any help with that, post back here what mobo maker and exact model number you have, and we can look up its manual and advise. But certainly, to use the GELID device you have, all your fans you plug into it must be of the 4-pin design.
As a side issue for your info, any mobo fan header can accept only ONE fan speed pulse signal to count. Two or more overlapping pulse signals would confuse it totally. So this device, and all good ones like it, will only send back to the mobo the speed signal from ONE of its fans. That is why only ONE of its output arms has all four wires to it, and why you should plug one of your fans into that output.
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