You’re the one who said that the deal was accept southern demands or be conquered by Britain. “They wouldn’t have gotten a deal otherwise, so apparently whatever benefit they received was a consequence of the Deal they made! (It was continuing independence from England. That was their benefit. )”
The Threat was from England, not from the South. Most of that Secessionist Independence movement was centered around New England, not the South. Much of the South wasn't even sure it wanted to separated from England until the Swamp Fox got the British to convince them that they did.