Shujee, The item you linked to is an ARGB Controller, but very basic. It gets power from a SATA power output connector from your PSU, and has several lighting patterns in it own "smarts" that you can choose using the three buttons on the module in the middle of the cable. Those are for Mode (pattern and changes), Speed (of changes to the display), and Colour (you can set a particular colour). NOTE that the ONLY way to change any light display is using that manual set of buttons. That means you have to arrange the items so that the cable from one end goes to a PSU output, and the other cable goes to your fan lighting connectors, and STILL somehow YOU must be able to reach the buttons on the middle box. There is no way to use software with this system. Moreover, although the page shows a manually-operated remote control box beside the basic unit, it does NOT say anything at all about that. So I expect that remote is NOT included in this system!
Some products on the market for what you want have been discontinued. But this one is available currently from Amazon.com for US$40
That's NOT cheap, unfortunately, but it does give you full control of your ARGB lights using the Cooler Master software utility MasterPlus+. Actually, this is the latest design that can work with the newest version of ARGB called Gen2. Your lights probably are the original version, and this unit CAN work with that, too.
Cooler Master also sells for much less money a controller designed like that cheap unit from Ali Express you linked to. It is a box with manual buttons you mount inside your case with connecting cables you need to be able to reach. Be careful, though. Cooler Master also sells units for plain RGB (4-pin, 12 VDC) systems, so be SURE to look for their Addressable RGB units.
The other option for you to consider is third-party ARGB Controller systems that DO include a hand-held manual remote control box. You do NOT get to use software for control, but the hand-held button box is easier to use than a box inside your case.
I just noticed you marked my earlier post Best Solution. Thanks.