The promises were generally kept. (Though I'm sure not always.)

Some 6,000 slaves fled to the British during the war, of whom circa 3,000 were evacuated as free after the war, mostly to Nova Scotia.

The officers of the Royal Navy were determined to keep their promises to these ex-slaves despite American protests. (The other roughly half of the slaves who had sought protection from British forces either died (many of disease) or had disappeared elsewhere before the end of the war).

Patriot forces also kept their promises at least generally. Some 500 Virginia slaves won freedom by serving in Patriot Armies during the Revolutionary War. (In 1782 there were only 2,000 free blacks in Virginia (1% of all blacks), though by 1800 there were 20,000 (7% of all blacks)), mostly due to the legalization of manumission, (which may have been a result of Revolutionary ideology).

Source: Alan Taylor, “Slavery and War in Virginia, 1772-1832, The Internal Enemy” 2013