After purchasing that geography book about the Wild Plains, the trio decided to take the rest of their time to lounge around in Tan village.
Their rush to reach Azure Lightning City wasn't exactly huge. Though, the trio didn't entirely lower their guards.
There was the possibility of that black robe man coming around for another kidnapping attempt. But at this point, the trio highly doubted it would happen.
Ever since leaving the Sword Sage Legacy cave, Cain had his Chaos Enhanced Sense passively spread out. For a few dozens of meters, he'll be able to perceive the slightest trace of power hostility.
And Cain had yet to detect anything from the black robe man. It was impossible that his Chaos Enhanced Sense couldn't perceive the black robe man, considering it did so several times already.
So their most logical conclusion was that the black robe man had already given up on trying to track them down.