As I suspected, you have been confused because the SAME two terms are used in DIFFERENT ways for two very different systems. There are 3-pin FANS, and 3-pin ARGB lighting cables, and they are VERY different systems and do NOT mix! Likewise, there are 4-pin FANS and 4-pin plain RGB lighting systems, and they ALSO do NOT mix! Your last post indicates you think that any 3-pin female (with holes) connector is for FAN motors, and any 4-pin female connector is for ARGB lights. Wrong!
Of those four photos you linked to:
First one is the female ARGB LIGHTING cable connector. See note below on the LAST photo.
Second photo is the 4-pin female FAN motor connector.
Third photo is the mobo 4-pin make plain RGB header you do NOT use for ANYTHING in your system.
Last photo is the 3-pin male ARGB mobo header that you DO use to connect the cable in your FIRST photo.
Your AIO system came with a 4-output ARGB Splitter for the three rad fans' lighting systems, and you have connected them all to this Splitter if I understand your comment about "daisy chain". Then that plugs into the mobo 3-pin ARGB header (Last photo above).
You have not posted any photos of a FAN header. I see, however, that you have connected a FAN connector to the mobo 4-pin CPU_FAN header and that makes the fan motors work. I presume, in fact, what you plugged into that header is the input arm of the three-output 4-pin FAN Splitter that also came with your AIO system. That is the correct place for that one. All three rad fans connect to outputs of that Splitter. The cable directly from the PUMP unit of your AIO system that ends in a 4-pin female fan connector should go to your mobo's AIO_PUMP header. The pump also has a cable that goes to a mobo USB2 header. Lastly, you must download the ASUS software utility (see p. 25 of the AIO manual) and install that (maybe you have that done already). It takes control of CPU cooling, communicating with the AIO system via that USB2 cable connection to the pump. I presume it also takes control of the lighting systems run by the mobo's ARGB header you have used.