To put briefly, some were treated okay, some were punished or had an ill reputation, some left to other colonies to escape persecution.

My main focus has been Revolutionary War in North Carolina so this is a small slice of the pie but I hope it helps. Even before the war ended the Revolutionary governments, usually Committees of Safeties, were persecuting loyalists or anyone suspected of being one. The loyalist or suspect would have to swear an oath or serve in the American militias, or face prison, exile. I've read that many after the Battle of Moore's Creek in February 1776 had received ill treatment from patriot neighbors including ousting them from there land and confiscating it. Some even faced forced enlistment to American regiments. The officers of the battle were sent to prisons and stayed there for upwards to 3 years, while some of the commoners went back to their faces, and faced their patriot neighbors' discontent.

Some families left immediately after the battle to New York or Canada to escape persecutions. In North Carolina, loyalism was squashed until Cornwallis came back to the Carolinas. Lets skip ahead to after the war, the NC government has just passed the Act of Pardon & Oblivion 1783 to help harmonize NC after the war. However, it didn't help much. The act was to allow loyalists to return home and get back their confiscated lands but the final clause in the Act almost said otherwise. Those that had served as commissioned officers, had left the state for more than a year or if you committed robbery, murder - you were exempt from the pardon. Loyalists had very small chances of getting back their confiscated lands, depending on their relations with their local courts. Claimants for their confiscated land were rarely accepts or received a small percentage of their property back. Some of the wealthy planters and merchants lost thousands pounds sterling from the war.

This left one option for some: exile. Nova Scotia was a popular place for loyalists, Florida too, but if one had the money the Caribbeans was another option. A lot of Loyalists did stay in North Carolina, depending on their circumstances. Some incorporated themselves into the new government, some became successful in their business/career.

References: Carole Troxler The Loyalist Experience in North Carolina

Robert Demond Loyalists in North Carolina during the Revolutionary War

Acts of Pardon and Oblivion 1783 North Carolina.