From your description when you plug the adapter in and only the CPU fan, the mobo believes the fan is running much faster, and you say this is actually true. Just to check: is that true? When you say the fan runs at full speed, do you mean merely that the screen display says it is 3500 rpm, or do you mean that you can tell that it really is running MUCH faster? Assuming it is true, for whatever reason the mobo is trying to feed full power to the fan, and appears to be receiving back from it a correct speed signal. All this is hard to understand given how the system is designed to operate.
First thing I suggest is to make sure you have the CPU fan plugged into the correct set of leads from the adapter. It MUST connect to the one set that has all four wires into it - black, blue, yellow AND green. Then be sure you have the connectors turned the right way - there really should be only one way to push them together. Also be sure you do plug the Moles connector into an output form the PSU.
Now, here is how it is supposed to work. With the adapter in place and all 3 fans connected, they all share via a parallel connection the Ground and +DC supply lines. The + DC line has a rapidly-pulsing (25 kHz) semi-square-wave signal with a "duty cycle" or "% on" that is varied by the mobo controller circuits. The single connector for the CPU fan has one additional line which carries from fan to mobo the fan speed signal, basically 2 pulses per fan revolution. The mobo uses that fan speed for two functions. The first is simply to display the speed for you. The other is to monitor it for any failure (indicated by no pulses at all) so that the system can be shut down quickly before the temperature of the CPU rises rapidly. In most mobos, the fan speed is NOT directly involved in the regulation of the speed.
Fan speed actually is controlled by a simple feedback control loop. There is a temperature sensor built into the CPU, feeding a signal to the mobo via one of its pins. The mobo monitors that and compares it to the setpoint entered in the BIOS Setup screens. Based on that difference, it varies the "% on" character of the PWM voltage signal sent out to the CPU fan, thus changing the fan speed. (Unknown to it, in your case there really are three fans using this same signal.) Now, what would cause the fan speed to increase? Only a rise in measured CPU temperature. What would cause the fan speed displayed on the screen to be higher? Only a higher fan speed signal coming from the fan. So, I am very intrigued by your statement that, in the scenario of using the adapter plus ONLY the CPU fan connected to it, suddenly the fan speed indication is much higher AND (asked you to verify) you agree that the fan speed really IS much higher. Merely inserting the adapter into the circuit should NOT have changed the actual CPU temperature nor altered the fan speed signal being sent to the mobo. By the way, when you did this, did you ALSO ensure that the adapter's connector to a Molex output connector from the PSU was hooked up? That is important because it appears they use that (and not the mobo pin connector) for the Ground lead.
Now, things could get fouled up if you try to use the wrong components, or if the connectors are wrong and the signals on the lines get mixed up. That is why I said to check the connections. But also, it is vital that ALL the fans be designed for PWM use. You can NOT use an older 3-pin fan on one of these adapters!
As a separate issue, I disagree with the concept here. The measured temperature of the CPU internally is the best way to govern the CPU's cooling fan operation. But to control the fans that cool the entire case, to me it makes more sense to use a temperature measurement in the case rather than inside the CPU. That is why mobos use a temperature sensor built into the mobo itself to run the feedback loop that controls at least one of its CASE_FAN connectors. In your case with only one CPU fan and two case fans, here is how I would use the adapter. NOTE: this only will work, as I said before, if BOTH of your case fans are designed for PWM control. Connect the leads marked for "mobo CPU connector" to the mobo's CASE_FAN connector that IS controlled by actual case (mobo sensor) temperature - read your mobo manual for this info. Connect the Molex connector to one of its mates from the CPU. Connect ONE case fan to the leads marked to go to the CPU fan (this one will provide the Case Fan speed signal), and the other case fan to one of the other two fan outputs. At the CPU cooler, just connect its fan directly to the mobo CPU_FAN pin header. In the BIOS, set both fan speed control systems (CPU and Case) to run automatically and, for now at least, leave their settings (like temperature targets and limits) at the default settings. In this scenario, the CPU fan will be controlled by the CPU temperature, and both case fans will be controlled by the temperature measured at the mobpo's built-in sensor.