The real problem here is that sellers of such devices quite wrongly misuse the terms "Splitter" and "Hub" as if they were the same thing. They are NOT! And interestingly, you got it right - that is a Splitter.
A SPLITTER is a simple device that simply connects all its fans in parallel to a mobo header. All of the power for the fans can come only from the header, so this limits the fan total load to the 1.0 A max current the header can supply. When using a Splitter you must find the max current draw spec for the fans and add them up to ensure the load does not exceed 1.0 A. A Splitter has one connection to the host mobo fan header, and two or more outputs with pins for plugging in fans. It may look like a collection of "arms" or a small circuit board. The one you linked to is a board with 9 outputs, which is very unusual.
You have spotted the most distinguishing feature between the two types of device. A HUB has those input and multiple output connections, but it also has a third cable that must plug into a power output from the PSU. A Hub gets power for all its fans from the PSU and does not load the mobo header, so it avoids the 1.0 A limit. BUT almost all hubs work only with 4-pin PWM fan systems. They MUST have a PWM signal supplied by the mobo host header, and they can only share that signal out to the PWM-type fans plugged into it. That system is how the speed of a 4-pin fan is controlled, but it cannot work for a 3-pin fan. A 3-pin fan plugged into such a unit can only run full speed all the time.
A fan header can deal with the speed signal sent back to it from only one fan. So for both Splitters and Hubs, the unit will only send back to its host header the speed signal from ONE fan, and ignore the rest. On the Splitter you linked to, one output is labelled "rpm"; it is the only one that will send its fan's rpm signal back to the host header.
For you, IF you have lots of fans and they all are of the new PWM 4-pin type, then you should use the Hub system supplied with your case. IF you have any 3-pin fans they cannot be controlled using that Hub. If that is your situation, you should be using a Splitter (like the one in your link) BUT you must check the total load of all fans connected to that - I'm sure you cannot come close to 9 fans! More likely you could connect 3 or 4 at max, depending on what the fan specs show. Then also you have to ensure that the one header you connect that Splitter to is configured to use Voltage Control Mode (aka DC Mode), and not PWM Mode.