If you want to achive asus software control of the fans in the case you do your best to connect them to the 4 chassis fan headers on the motherboard. Making sure that the fans do not go over the amperage max for the MB fan connectors. This is usually possible, though not always easy, or might require some adaption, or extention.
I far prefer this method, because with motherboard control, and the software you can get automated control of the fan based on a thermal profile.
Weird Stuff:
The 4 pin asus MB chassis fan (not cpu fan which is PWM) are more often not PWM controlled, but 4Pin, which can be confusing, because 4pin should mean PWM :-(. So a 3pin put in the correct alignment for the key slot thing, should work in the 4 pin slots, and fully control the speed. Check the manuel, and what people are saying about the PWM (or not) to verify. I only know about this from 4 boards so far.
It all is generally compatable:
So basically 3pin and 4pin Motherboard header pins are all compatable, and key in similarity.
A real 4pin PWM fan put into a 3pin slot will be controlled only via changes in the power going to it, not via actual PWM pulses sent on the missing pwm line.
A 3 Pin fan will Operate on a 4pin real PWM header also, but only at full speed.
Add in Asus having 4pin headers for chassis fans that are not real PWM controlled. It still all works. . . So a simple 3pin MB header type of connection , should still have full control, in the asus 4Pin Chassis fan locations.
The "Molex" (+5v Ground Ground +12V) connectors/adapters, the 4pin larger connections would be the connection used for connecting the fans to a PSU (with molex) Or to possible PSU "Fan-Only" type of connections (some PSUs). Or to connect to some seperate fan controllers. The ones shown are adapters with Passthrough capability, so you can connect something else with the Molex and still power the fan, or to chain more than one together from a single available molex connection.
Basic Idea put 12V on the fan in the correct polarity. (the 5V item on the same is left unconnected)
Also some cases have manuel control of fans, built into the case itself. It is more rare that case control of fans , is a full controller that also can create thermal profiles. Cases have used both MB sized connections, and the big Molex connectors to connect to the controllers. I do not see where the case you have chosen has that stuff. So it kind of makes it easier, because you do not have to decide what method to use.
In the Molex (the big 4 pin plastic connectors)
Red is +5V
Black is common ground or 0V
Yellow is +12V
And the fans usually use +12v and the ground.
On the Fan wiring, they are more often using
Red for the +voltage (yea which is 12v)
Black for the common ground 0V
Yellow for the RPM line back to the MB.
You can see easily what is going on, with these Molex fan adapters, with the yellow +12Volt line headed to the Red +12V line of the fan.
This changing the colors is why it is very usefull to read the manuels, and/or have a voltmeter to verify things.