Yeah, I would expect fans to come on first, then AC if fans are insufficient. Interestingly, a friend of mine drove his Cayenne S E-Hybrid to my house, about 1 week after I got my Outlander PHEV, and at the time, I hadn't yet installed my Level 2 EVSE. I plugged my Level 1 (120V) EVSE into his Cayenne, and the front grill slats opened up and the fans and pumps started up to cool the battery. It was an abnormally hot day. Ambient temp was around 35C, and the car had just been driven, but still, it was only Level 1! Now I have never charged my Outlander PHEV in those types of conditions (haven't had a chance to, because it hasn't been this hot recently) but I really wonder if there would be any sort of cooling delivered to the battery at all when it gets that hot, whether via fans or AC or both.
I am a bit preplexed by Mitsubishi's decision to go with air cooling rather than liquid cooling. Liquids generally have a higher heat capacity than air, and can deliver more consistent temperatures, especially if the pumps/fans are on. Obviously this isn't a Leaf, with its only passive air cooling, and at least has active fans and AC systems helping to cool the battery, but if the fans aren't coming on during L2 charging on hot days, I'm not sure that the system is doing its job (which is why I asked if anyone has ever heard the fans or compressors come on during those conditions).