There were articles of faith in the early church that had different intrepretations by individuals and groups. For instance,humanity and divinity of Christ. There were at first all sorts of opinions and it became confusing and people wanted to know what exactly was the truth. Case in question is the Arian controversy. So then the Church had a council of bishops to discuss and decide what was true and what wasn’t. Then they met, clearified the faith, and then passed this on to the entire church, and said that the other interpretations were not acceptable any longer. Those who did not accept the definition given by the bishops, were considered heretics and not to be listened to.
Paul in one of his letters also gave the same warning where he mentioned someone by name and that they were not to be listened to because they were teaching false doctrine. So this type of correction actually happened from the beginning.
So an article of the faith is usually never defined by a council until it is first challanged.
Whether these departures were branches of the old vine, or completely new vines, is not a option in view of the effects. They are considered new manmade churches because truth is one, not multiple versions of one. The church may not say in every individual situation that this or that church is no longer connected and constitutes a different church. In other words the trigger isn’t always pulled right away, but some time may be given for deliberation. For example: The church did not respond right away to Martin Luther because they thought it would all go away if the situation were given time.
In the Arian dispute and some others, there were real bishops involved who otherwise upheld the teachings. In the Reformation, there were real bishops involved but not leading, and they were departing from a number of important teachings.