You've missed telling us half the info. The "single ARGB Header" is on WHICH mobo? Its manual should specify the max current limit available from the header.
The Cooler Master website shows that the Cooler Master MasterFan MF120 Halo units' LIGHTS only pull 0.55 A typical, and 0.80 A max current PER FAN. So to be safe you would need a mobo header able to supply 8 A max, and I doubt your mobo can do that from ONE ARGB header. IF your mobo has TWO such headers, you might well be able to connect two groups of four fans each using two Splitters, assuming each header can supply more than 4 A.
If you have only ONE ARGB header on your mobo to work with, then you will need something else able to supply the power. You do NOT need a third-party CONTROLLER for the lights IF your mobo does have an ARGB header. You DO need an ARGB HUB that gets its control signals from a mobo lighting header, but gets all the power for those lights directly from a PSU output. Such items typically use a SATA power output connector from the PSU, and that connector system has a limit of 4.5 A max current from the 5 VDC supply lines from PSU to Hub. So you actually would need TWO of those Hubs (max of 5 fans' lights at 0.8 A each per Hub) to power all those fans' lights. Do not be misled by some of these units that offer 10 or 12 output ports on a lighting Hub - you cannot power that many of your fans from one Hub.
To get the ARGB control signal from a single mobo header to TWO of these Hubs, you do need a simple 2-output ARGB Splitter like this
Note that this is for ARGB with THREE holes on each connector. Also note that it comes with little gender-changer adapters to convert its four outputs to males (with pins). I suggest you install those in only two of the outputs (for your two Hubs) and tape up the other two unused outputs. You CAN feed both Hubs from one header because the Hubs are only taking the Digital Control Line signal from the header, and NOT overloading the power lines of the header.
You have not asked about the fan MOTORS. One way to do all this is to get Hubs that really are TWO Hub devices in one unit, like this one form Cooler Master
That really has two separate Hubs in one unit - a Hub for 4-pin PWM fan MOTORS, and a Hub for 3-pin ARGB LIGHTS. Each half works independently. The MOTOR half uses 12 VDC power and a mobo fan header for control signals, while the LIGHTING half uses 5 VDC power and control signals from an ARGB lighting header. If you get two of these you can use one if them to connect some lighting cables AND the motor cables from six of your case ventilation fans. But wait - you have seven such fans, right? Well, also get one simple fan SPLITTER like this
OK, that's a 2-pack. Use one of them to connect TWO of your fans' motor cables to one of the Hub's motor ports, so you have all seven connected to it. The 4.5 A max current limits imposed by the SATA power connector for the 12 VDC lines are separate from that limit for the 5 VDC lines, so there is no issue limit there. And the specs for your fans are 0.25 A per motor max, with a top-end limit of 0.37 A, so seven of those is a max normally of 1.75 A, extreme conditions up to 2.6 A. Again, not a load problem doing this. In addition, of course, you plug into that Hub's ARGB ports the lighting cables from only FIVE of them (comes to 4.0 A max lighting current). For this Hub you connect its MB ARGB port to one output arm of your ARGB Splitter, and from its MB PWM port you run a cable to one mobo SYS_FAN header to pick up the PWM control signal. This way ALL of your seven case ventilation fans are powered and controlled by one SYS_FAN header, while five of them have their lights also handled by that Hub. The SYS_FAN header needs to be configured to use PWM Mode, to use the motherboard temperature sensor, and to use the default standard automatic temperature control scheme at the start.
For the three fans on the rad of your AIO system, that kit will already include some means (a Splitter perhaps, or a multi-head cable) of connecting the MOTORS to power and control. Control of these will be done either by the CPU_FAN header or by some software utility like MasterPlus+. You do not need any connection to a hub for those three fans' motors. However, you DO need the second Hub to connect the LIGHTING cables from those three fans PLUS those from two of your case vent fans to power and control. This second Hub's MB ARGB cable goes to the second output arm of your ARGB Splitter. Since you will not be using this hub for fan MOTORS, you do not need to connect a cable from its MB PWM port to a mobo fan header. Lastly, the lighting cables from two of your case fans can come to ports on this Hub - it will be doing exactly the same thing as the other Hub for the lights.
This way ALL of your lighted fans can be powered and controlled from the mobo. Three AIO Rad fans are powered from the CPU_FAN header or something like that. Seven case vent fans are powered and controlled from one Hub (and a Splitter) connected to a single SYS_FAN header, with the12 VDC power for their motors coming from the PSU via the first Hub. The LIGHTS in all ten fans are powered and controlled from TWO hubs (five fans' lights each), both using the Digital Control Line signal from one mobo ARGB header, and both using 5 VDC power from the PSU, again. No power limits are exceeded. I expect that the MasterPlus+ software tool you get with the AIO system will allow you to do BOTH fan control and lighting control of all of these fans with that one software tool.