I'm starting to think if you were a fourth century bishop and you didn't get exiled, you just weren't doing your job. Cyril "was a gentle man, conciliatory by nature..." (Burns, p. 125) yet he spent the majority of his thirty-five years as bishop in exile. He survived at least four emperors and was exiled and restored three times. That's not a career track; it's a carnival ride.
Arianism was the big heresy at the time, though of course not everyone saw it as heresy. Cyril kept looking for the middle ground between the belief that Jesus was purely human, or purely divine, or inexplicably both. The latter was the orthodox view, and as such his own, but he was still willing to compromise. Not so his rivals, especially Acacius, Bishop of Caesarea. Acacius got a local synod to boot him to Tarsus, probably because Jerusalem seemed to be gaining prominence over Caesarea as a diocese. An ecumenical council restored Cyril after a couple of years.
Acacius then made complaints to the Emperor Constans, who re-exiled Cyril. Emperor Julian came along and reinstated him. He only lasted two years and failed in his attempt to rebuild the Temple in Jerusalem, just as Cyril had warned him. Nonetheless, the Emperor Valens reversed all Julian's reinstatements, including Cyril. Fifteen years later he was reinstated by the Emperor Theodosius, but by then, Jersualem had gone berserk. Gregory of Nyssa showed up to help him restore order, but instead just wrote a sort of travel advisory for would-be pilgrims, cautioning them to find some other place to which to pilgrimate. [Yeah, I said pilgrimate.]
Revenge is a slow meal to prepare. The second ecumenical Council of the Church was held at Constantinople in 381. At it, Cyril participated in the revision of the Nicene Creed, adding phrases like "begotten from the Father before all ages," "he came down from the heavens," "was incarnate from the Holy Spirit and the Virgin Mary," and "one in being with the Father." This cinched up any Arian ambiguity, making sure that the Orthodox view of the dual nature of Christ would be official and officially enforced doctrine.