Basically, I repeat my prior post. As I suspected, the fans you have use a non-standard SIX-pin connector on the end of ONE cable per fan. The only way to make any connections from that to any mobo header would be to KNOW the details of all six connector pins, and then make your own adapters to make connections. There are no off-the-shelf adapters for this.
The system includes a Controller box / ARGB Hub, a manual hand-held box, and a couple of cables. The two boxes appear to have controls only for the lights in the fan frames. There is no indication that you can connect to them a fan MOTOR SPEED signal from a mobo fan header. Nor is there any sign that the manual box has controls for fan motor speeds, so they MAY only work at one speed always. All its buttons appear to relate solely to lighting display features.
The cable from the Controller box with two 3-hole connectors on it is ONLY for connecting to a mobo ARGB Header so the mobo can control the LIGHTS. But your mobo does NOT have one of those headers, as you say. The only way you could feed an ARGB control signal to that box using your keyboard, rather than the manual box, would be to buy a third-party ARGB Controller that includes its own maker's software utility for that purpose. Then you could connect the ARGB control signal from that Controller to the cable with 3-hole connectors from your Control Box with this set. Then you use the green button at upper left labelled "MB", I suspect, to tell it to let the external signal (from your third-party Controller) take over lighting control.