This is a fine example of why I complain about the way various makers use or misuse the terms. But I have to concede that the way I use the words is not decreed by anybody.
To me, a fan SPLITTER is the simple device that connects several fans in parallel to the signals from a host mobo fan header, and that's all it does. It has NO connection to any other power source, so the power for ALL of the fans on a SPLITTER must come from the fan header and is subject to that header's limit, normally 1.0 A max total. A fan HUB is a different device and can be identified by the fact that it has a third type of connection - one arm that MUST be plugged into a power output (either 4-pin Molex or SATA) from the PSU. That is the source of power for ALL of the fans connected to the Hub, and it draws NO power from the host header. It does collect the PWM signal from the header and distribute that to all of its fans, but that does not overload that header line. And it does return to the header the speed signal from ONE of its ports, just as a Splitter does. However, since the HUB merely distributes the PWM signal to its fans via Pin #4, and also a fixed +12 VDC power source on Pin #2 for all its fans, it can ONLY control the speed of 4-pin (PWM type) fans and ONLY if it gets the PWM signal from the host header. Thus a HUB can NOT control the speed of any 3-pin fan, no more than a PWM Mode mobo header can.
A 3-pin fan can ONLY be controlled for speed if its mobo header is using the older Voltage Control Mode in which changing the VOLTAGE on Pin #2 is the MODE of controlling speed. A 4-pin fan normally receives instead a fixed 12 VDC supply on Pin #2 and an additional PWM signal which is used inside the fan by a special chip to modify the current from that power source through the windings to effect control of fan speed. So the rule is (IF you use my way of labeling these two different devices) you can use a HUB only with a mobo header that is using PWM Mode to control, and ONLY if the fans are all of the 4-pin PWM type that has the special chip to use that signal. IF you are using 3-pin fans the mobo header can ONLY control their speeds if it is using the older Voltage Control Mode (aka DC Mode), and that means you can NOT use a HUB for this situation, you must use a SPLITTER instead. Let me say right here that I know of ONE Hub that does not follow this "rule". The Phanteks PWM Hub is different because it "converts" from the PWM system it MUST have from its host header and creates its own group of six 3-pin ports that DO use the older Voltage Control Mode and thus CAN control 3-pin fans. Also we should note that one of the backwards compatibility features of the new PWM fan design is that its speed CAN be controlled by the older Voltage Control Mode, even though technically this is not quite ideal.
So, OP, that Deepcool FH-04 unit you noted is a SPLITTER the way I use the term. It has NO access to external power, and depends entirely on the mobo header for power. IF you are concerned that 0.9 A total for 3 fans is getting too close to the 1.0 A limit of a mobo header, then this is NOT the HUB you want. A basic HUB might look like a group of arms, like this one with 3 outputs
https://www.newegg.com/black-en-labs-11-15-cable-splitters/p/1W7-004Z-00039?Description=fan Hub&cm_re=fan_Hub--9SIACJF5497318--Product
This one has five outputs and looks like a small circuit board. You do NOT need to connect your CPU fan to the port labelled for that - it is just the only output that sends back to the host mobo header the speed signal of its fan.
https://www.newegg.com/p/1W7-005X-00071?Description=fan Hub&cm_re=fan_Hub--1W7-005X-00071--Product
If you want a closed box type with ports, here's an example, the Deepcool FH-10 with 10 fan ports and a SATA power connection.
https://www.newegg.com/p/N82E16811990016?Description=fan Hub&cm_re=fan_Hub--11-990-016--Product
Your two fans included with the Corsair Carbide 275R case are a different question. I cannot find a spec for exactly what fans those are, but I suspect them may be 3-pin models. Look closely at their fan connectors. Do the have three holes in them, or four? If THREE holes, then these are 3-pin fans that can ONLY be connected together to a header using a SPLITTER (like the FH-04 model you noted, or others), AND that header MUST be configured to use the DC Mode for control. IF the two case fans have FOUR holes in their connectors, then you CAN plug them into the SAME HUB you are going to use for your ThermalTake fans, and have them all share the same control signal from a single mobo header using PWM Mode. That works because the HUB does not pull its power from the header with its 1.0 A limit - the HUB get power from the PSU.