More than likely a setting in the ECM, I have used trucks that had a setting that kicked the engine fan on as soon as the pto was engaged, regardless of the engine temperature, and would stay on as long as the pto was engaged.
I think turning on the a/c turns on the fan too. Might be running warm at idle, and takes a couple gears to cool off, not unusual. Garbage trucks with the pto running have the fan running, to cool the hydraulic oil. It's really annoying.