Do NOT buy that one you linked to. It is what I would call a HUB. It has five outputs (attractive to you) but it does NOT work as a Splitter. This Hub gets all the power for its fans from the PSU directly, via that extra arm with the male 4-pin Molex connector (even though it has 2 pins). Thus the ONLY power supplied to the fans (each on their respective Pins 1 and 2) is a fixed 12 VDC, and ALL your 3-pin fans will run at full speed all the time. This unit is designed to work with ONLY 4-pin fans. With them it works because the one arm that plugs into a mobo 4-pin header must pick up the PWM signal on header Pin #4 and then distribute that to all the fans. A 4-pin fan will use that for speed control, but your 3-pin fans can not do that.
A Splitter works differently and is the ONLY way to combine 3-pin fans onto a header. It depends on the mobo header to operate in Voltage Control Mode and supply variable voltage on Pin #2 of the header. Then that voltage is shared out to all the fans on the Splitter. The limit is that one header can supply up to 1.0 amp total to ALL the fans attached to it. Now, most common case vent fans today consume from 0.1 to 0.25 amps, so four on one header (via a Splitter) is OK. A Splitter does NOT have that extra arm that connects to a PSU output.
Using a Splitter requires that the mobo header you plug it into operates in Voltage Control Mode. Many do these days, whether they have 3 pins or 4 pins. And in fact, whether you use 3-pin or 4-pin SPLITTERS does not matter when you use them to connect 3-pin fans to such a header. But just to be sure this will work for you, post back here what fans you have, and exactly what mobo maker and model number, so we can check what its headers do, and check the current draw specs of the fans.
Now, what SPLITTER system do you need for 4 fans to one header? Here's an example of one with two outputs.
https://www.newegg.com/Product/Product.aspx?Item=N82E16812423168&cm_re=fan_splitter-_-12-423-168-_-Product
You should buy THREE of these. "Stack" them by plugging two of them into the output arms of the third one. This gives you 4 outputs from one header.