That's not what happens. Iron Bull is pretty much always a Qun loyalists. Circumstances force that to change if you save the Chargers where he gets expelled and learns to deal with it. If you don't save them, or don't do the quest, he remains obedient, gets a debriefing/re-education period in between DAI and Trespasser, and thus betrays you no matter what because it is a demand of the Qun. As he says himself; nothing personal, bas.