12v PWM Fan Seems to Be Running Inversely of What It Should Be
I suspect that your new fan requires an inverted PWM signal compared to what the board is providing -- that'd explain why it'd control "backwards".  I'd use a 78L05, one section of a 74HC04 or equivalent inverter IC, a couple of 100nF ceramic caps, and a 4-pin 0.1" header and socket to fabricobble an inverter-adapter for the PWM on perfboard,
 as in the schematic below (presuming your fans follow the PC motherboard PWM fan interface standard, that is):







simulate this circuit &ndash; Schematic created using CircuitLab