There was not a systematic 'terror' like the one that occurred in France. However there were numerous examples of mob violence and vengeance against Tories (the American Revolution's version of 'counterrevolutionaries') before, during, and after the war:

Before the Revolution, or at least in the early stages, the Sons of Liberty committed acts that could be considered 'terrorism': tar and feathering tax collectors; destroying the Governor's Mansion by mob in Massachusetts, etc.

George Clinton, first post-Colonial Governor of New York (and later fourth Vice President of the US), gained political power partly by leading mobs that terrorized suspected Tories and confiscating their properties.

After the British occupation of Philadelphia, angry mobs in that city committed acts of violence against Tories and even threatened members of the Continental Army stationed there to maintain the peace. This influenced General Benedict Arnold's decision to defect to the British in light of the general mob violence and unruliness of the American civilians.

In 1793, the French Minister to the United States, 'Citizen' Genet, incited angry mobs directed against President Washington due to Washington's insistence that America remain neutral, rather than forging an alliance with France against Britain. Vice President John Adams described in his diary his fears that at any moment an angry mob would seize Washington and murder him.

For an interesting fictional account, read 'Oliver Wiswell' by Kenneth Roberts, about the trevails of Boston Loyalists during the Revolution. (Also Robert's book Arundel features a sympathetic account of the pre-treasonous career of Benedict Arnold).

Follow up question, did flight mitigate this? That is to say, loyalists returning to Europe or going to Canada.