I think Karadjgne is on the right track. Unfortunately the Antec website for that case does NOT provide a link to the proper manual, nor could I find one in a net search. So we're reduced to speculating on what can be done.
First, what is common or "normal" in the field of ARGB Fans currently (and I am sure the four fans included with that case are the Antec Prizm 120 ARGB models). Such fans normally have two cables from them - one ending in a four-pin (hole) female standard fan connector for the PWM-type fan motor, and another wider female one ending in a connector with space for 4 pins in a line but with one hole (pin) missing for the ARGB lighting units in the fan frame. Each of these plugs into different appropriate headers on the mobo IF yours has them. Otherwise they (especially the ARGB connectors) can connect to ports on a Controller box supplied usually by the fan maker.
What the photos and captions of the web page show is a printed circuit board included in the case with six six-pin output ports for "ARGB Fan " connections, one header for a "Motherboard Sync Connector", one 2-pin header for a "LED I/O Port Connector" with an item plugged into it labelled "FAN", and a "Built-in LED Controller" header that has the label "Power" on the board. It has no standard 4-pin fan or 3-pin ARGB ports.
This is what I suspect that board does. I suggest you contact Antec Sales or Tech Support to check this and ask where to get the real and complete case manual. I think each of the fans supplied with this case actually has a "non-standard"single 6-wire cable from it that plugs into the controller board ports (six available). My guess is that these are solely for the ARGB lights in each fan, and that the fan MOTOR cable still is separate. I suspect the two-wire connector labelled "FAN" on the top right header is from the case's front top LED control button and that is how you change the light displays. Since your mobo has no ARGB header on it, you can not use the supplied extra cable to connect this board to a mobo ARGB header for the "Sync" function.
That leaves four standard 4-pin PWM fan cables to connect somewhere. I believe you do NOT need that extra Phanteks fan Hub you mentioned. These fans have specs of 0.18 A max current per fan, or a total of 0.72 A for four if they all are connected to a single mobo fan header. That is quite acceptable. All you need for that is a simple SPLITTER with four outputs. In my way of using the terms, a SPLITTER only has two types of connections, It has one "arm" that plugs into a mobo header to get both power and control signals for all its fans from that header, and thus is subject to the header's normal 1.0 A max. It has two or more (I'll link to a one with four) outputs for the fans. A HUB is a different device like the Phanteks unit you linked to. The difference is that it has an extra third "arm" that must connect to a SATA power output from the PSU for all the fan power supply, thus NOT loading up the mobo header. Here's a Splitter that looks like a circuit board with four outputs, and needs to be fastened down so it does not make accidental contact and cause a short circuit.
https://www.newegg.com/p/N82E168824..._re=coboc_fan_splitter-_-82-422-016-_-Product
One of its ports is labelled for the CPU fan, but ignore that. Just use this for all four of your fans. Note one detail of any Splitter or Hub. A mobo fan header can deal with the speed signal of only ONE fan sent back to it - more causes confusion, wrong readings and error messages. So this Splitter will send back to its host port only the speed of the one fan plugged into the port called "CPU" and ignore the others. You will never "see" the speeds of the other three fans. But this has NO impact on ability to control those fans. All four of them will operate at the same speeds.
Your mobo has two CHA_FAN headers. So as an alternative if you want to create two separate groups of them, you could plug the front 3 into one header using that Splitter and the rear one into the other header. OR you could use two different common 2-output Splitters, and connect two fans to each header.
https://www.newegg.com/p/N82E168124..._re=coboc_fan_splitter-_-12-423-160-_-Product
That one has 6" long output arms, but there's another model with 12" arms.