Yep, non-standard fans for a computer system. The colour codes you cite are not "normal". For a new-style computer 4-pin PWM type fan, the wires normally are
Pin 1 Black Ground
Pin 2 Yellow +12 VDC constant voltage
Pin 3 Green Speed pulses signal sent back to header
Pin 4 Blue PWM signal to fan
On SOME systems the colour sequence instead is Black - Red - Yellow - Blue. The first three of these is the same as on all 3-pin fans, and then the fourth pin is blue wire.
Your fans do not use these colour codes.
Now, you said the fans work when you connect 12 VDC power to Black and Red. I assume you did NEGATIVE to Black, and positive to Red. You also say that the fans run slower at reduced voltage. This IS normal. Because the new PWM fans were designed for maximum compatibility with the older 3-pin fan system, they are normally supplied with fixed 12 VDC power plus a PWM signal. Inside the fan a small chip uses the PWM signal to modify the flow of current from that supply through the windings to reduce speed. IF you connect such a fan to an older 3-pin header which cannot do those signals, the fan gets NO PWM signal to use, so it cannot modify current flow. But the header does supply power at VARYING Voltage, not fixed 12 VDC, so the fan speed IS controlled in this way. Your seller did not understand this.
IF the WHITE wire on your fans really is solely for the PWM signal as your seller says, then certainly connecting a +12 VDC supply to that could damage the fan's internals. So do NOT try that. THEN, if you assune the seller is correct about the proper finction of the WHITE wire, you could slip those three wires into a female 4-pin fan connector body with the white on the Pin #4 end. Since your info is that the fan has NO speed pulse signal output to go back to the header, then NONE of your wires would go to the Pin #3 slot of the connector. With those connections made, if you plug that into a mobo 4-pin header that is configured to use the new 4-pin PWM Mode of control, the header should be able to control the fan speed. Alternatively, if you plug it into a 3-pin mobo header, that ALSO should control the fan speed as I said above. But in both cases you simply would not have any speed reading at the mobo header, and it MIGHT give you a Fan Failed warning because it has zero speed reported. NOTE that the header does NOT need or use the speed signal to control fan speed. It uses that only to detect fan failure.
FYI a small note since you obviously have some knowlege in this field. PWM control of fan motor speeds in a computer is NOT done the same as a PWM speed control system for larger motors in industry. In those systems the electrical supply fed to a motor IS already modified into a fast pulsing DC Voltage at the motor Controller unit. That design could not be adapted easily to the older 3-pin fan system in computers for easy compatibility, so it was changed for computer fans. For this reason computer 4-pin fan makers specifically tell you NOT to try to feed power to their fans from a common industrial PWM speed control system.