I suspect you misunderstand, although the case's manual does not provide the detail needed. The fans supplied with the case MAY come with standard 3-pin or 4-pin female connectors on the ends of their wires, allowing them to be plugged into mobo CHA_FAN headers. Or, they may come with larger 4-pin Molex male connectors, or even something else. It depends on the output connectors provided with the case's built-in fan control system. But for the moment, let's assume they have either 3-pin or 4-pin standard female fan connectors on them.
If they are set that way, you can chose either the case's control system or control by mobo headers. The case's system basically allows you to set the fans' speeds manually and leaves you with the responsibility to determine what fan speeds you need at different times as you use the system. Connecting fans to the mobo CHA_FAN headers will allow the mobo's automatic control system to control those fans for you, adjusting to system workload according to measured temperatures.
I am sure you will NOT have the option to connect the case's fan control system to a mobo CHA_FAN header. I expect the power input connector to the case's control module will be either a 4-pin Molex male or a SATA Power input connector, either of which can only connect to a PSU power output. There really is no adapter to allow you to connect one of those to a mobo fan header, and you would not want to do that, anyway. If your fans are under mobo automatic control, there is no use interfering by adding case pushbuttons to modify that control system.
Whether you can actually control those case fans using the mobo CHA_FAN headers is not clear. Your mobo's fan headers have 4 pins and are labeled as using PWM Mode. If that is true, they can NOT control the speed of a 3-pin fan, and that is often what is included in a case. Unfortunately, your case's specs and manual do not tell us the fan type included. There's also another unknown. SOME mobos have 4-pin fan headers that can be configured in BIOS Setup to use either 4-pin PWM Mode, or 3-pin DC Mode. Your mobo's manual shows that at least the CPU _FAN header has this capability, but it is not absolutely clear whether that also apples to the CHA_FAN headers used for case ventilation fans. So they MAY work for 3-pin fans if that setting is actually available.
Personally, I prefer to connect all case ventilation fans to mobo CHA_FAN headers and let the mobo's automatic control system do the job for me. However, I know that some users prefer to exercise control themselves, and your case's built-in fan buttons offer you that choice. But you can't do both.