Frankly, Law would have followed along even without the indication that he should; while he's done with patching up Cora's stab wound, it's not like he's going to let him out of his sight.

Besides... he'd like to have some select words with Reiju, too. Which is why, when Cora opens the discussion on devil fruits, he's quick to add,

"It would have been better for it to not be a surprise. Reiju-ya, I thought you actually knew something about tactics." Somehow, he manages to make that sound incredibly accusatory — hiding your weaknesses is a good move, except when it can get you and others killed. In that case, it's just stupid. He didn't think she was stupid.