I don't think this is explicitly discussed in DE:HR, but I think there are enough clues to more-or-less figure this one out.
Hugh Darrow's signal makes unauthorized use of the Illuminati's "upgraded" bio-chips designed by the kidnapped Sarif employees and distributed by 泰永 through the worldwide network of LIMB clinics.
Anyone who doesn't have that particular chip software is safe from the signal. Adam Jenson is immune (despite having augs) either because he never obtained the chip from a clinic or because Megan Reed disabled it for him.
Some plausible possibilities are that:
Sarif's augs are experimental and custom made, so the firmware isn't compatible with the "upgrade" (this seems likely, since it looks different than any other augs seen anywhere else in the world).
He suspected that the recall was bogus and didn't go to a clinic to get the fix.
Sarif got the upgrade, but not from LIMB (possibly done at Sarif Industries itself) and the chips themselves needed to be tampered with by LIMB on-site in order for it to have the back door functional (which would make sense, otherwise reverse engineering by other bio-tech firms might uncover the built-in vulnerabilities).
Darrow customized the signal to spare his old friend from going mad (and potentially being killed).