In short, that is why it does not work with the Antminer S4 controller.
I think the easiest way for you would be to have another fan model.
In that guide, the cooling fan manufactured by Sanyo is a good one.
https://support.myrig.com/hc/en-us/articles/204199879-Antminer-S4-fan-specification-and-possible-replacement-fans
It is does not have reversed PWM signal.
I used to have that Sanyo as a cooling fan for my Avalon 6.0 back in the days I had that miner.
Very good quality fan.
Very grateful for your answer brother !!! How unfortunate that he bought the one that was not, I should ask before doing it ...