It would help if you tell us the maker and exact model of your mobo so we can look up its specs. Why? The label you cite includes "V2". Now, that bit is used to label the latest iteration of ARGB systems, BUT it is NOT clear whether YOUR mobo is using it that way. The original ARGB system is significantly different from the new V2 version. It is not clear from your post which you have, so I'll describe both. I will NOT talk about the simpler 4-pin plain RGB system. You are correct that you must NOT try to connect a 3-pin ARGB lighting unit to any 4-pin plain RGB header.
Note that, when I speak of mobo Controllers and Headers, the same applies to third-party Controllers. IF you use an ARGB SPLLTTER that merely connects several strips in parallel to one header, each strip will simply receive the SAME set of signals. IF you use an ARGB HUB, the same applies EXCEPT that a HUB gets power for all its light output ports directly from the PSU, so the POWER limit of a mobo header does NOT apply in this case. Note also that on many mobos and third-part Controllers there may be more than one output header or port. In those cases the makers MAY treat all such outputs are mere duplicates of each other, OR may have each output port use its own separate Controller chip so each port sends out different signals, often with the option to make all the outputs identical or "synchronized".
Original Addressable RGB (aka ARGB) System
This is the system that uses THREE wires and pins / holes in connectors. Those wires consist of two common power lines (+5 VDC and Ground) and a common Digital Control Line. Along any ARGB light strip (or in a fan frame) all the LED's are grouped in Nodes. Each Node contains one each of three LED light sources (Red, Green, Blue) plus a node controller chip. All units draw power from the common power lines. Each Node's controller chip listens to the Digital Control line. The mobo port controller sends out on that line a series of instruction packets, each with an address. Along the line an individual Node controller chip responds only to an address packet with its unique address and does what it is told with its own three LED's. Thus at any one moment every Node group on a strip can be a different colour, and of course the instruction packets can be changed any time to other patterns. In the original ARGB system there is a means for the mobo Controller chip to inquire about the TOTAL number of Nodes in the entire lengthy strip of lights connected to it (whether that is one string or several connected in a daisy chain). On that basis it sets itself up to send out that many different instruction packets in each full set of packets, then repeat. IF you connect two or more strips in parallel to a single ARGB output header, each strip receives exactly the same sets of signals, so each separate strip will do exactly the same as all the others it is grouped with. The limits of the header output typically are twofold: a limit on the total number of LED Nodes (often 240 max) imposed by the addressing limit of the system, and a limit on the max total AMPS of electrical power available. Ideally this might match with that addressing limit allowing for the max amps per LED Node, but that is not always the case.
ARGB V2 System
This is the newest version, and some details are NPT well publicized, so we are left to speculate a bit and some details may NOT be the same from one maker to another. This does use exactly the same wiring and connectors because the difference is solely in the details of the digital instruction packets. One thing is certain. To get this to work competely, you need BOTH the Controller (in the mobo header or thrid party Controller) AND the lighting STRIP (or fan frame) to be of this new design version. An original-version strip plugged into a V2 header cannot be controlled and will not work. For that reason, to simplify introduction of this design in the established market almost all makers offer you an option in its setup configuration. You may set it to use the new V2 system, in which case ALL your light units must also be V2. OR you may set it to use the older Original version, in which case the displays it generates can only be of that versions abilties, but ALL ARGB light strings will work that way.
ARGB V2 differs from the Original design in one important point. No matter how you connect several light strips to a single output port or header (whether in parallel using a Splittter or Hub, or by a daisy-chain arrangement) it can treat EACH light strip separately. The detection and control system has a way to identify each connected light strip as a separate device. The instruction packets sent out contain addresses the identify separately the NODE for the packet AND the LIGHT STRIP that Node is in. Thus not only can each Node of one strip be different at any one moment, but also the pattern of each separate light strip can be different from the pattern of others. For example, if you were to connect three lighting units (strips or fans) to one header or port in an Original ARGB system and have it send out signals for a moving rainbow effect, each seprate light unit would do the same thing, and you'd get three identical moving rainbows. But in a V2 system you could get ONE rainbow stretched over all three light units as if they were one long unit. Or, you could have three different lighting patterns going on at the same time, one on each strip.
The LIMITS of this system are a bit differnet. There still are max limits on the number of LED Nodes you can have on one output, and on the max Amps power load. There also is a limit on the max number of light strips it can handle as separate strips. ONE mobo maker I saw specified its ARGB V2 header can deal with up to FOUR separate lighting units per header. I have not seen clear specs from some others, so I am not sure whether all V2 system use this limit.
OP, you asked the max number of fans you can connect together on ONE lighting header. Certainly you will need to know the COUNT of LED's (nodes) in each fan frame, and the max Amps of power the LIGHTS ONLY in that frame can consume. (NOTE that the lights are separate from the fan motor, so you need the LIGHTS Amps and NOT the amps for the motor!) IF you have the new V2 version of both header and lighting units, then you may be limited to four units per header. But if you are using only the older Original version, that limit will not apply.
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