Mal does recognize this, and eventually, on the opposite side of the enclosed area, he dismounts, slowing and cooling Tequila down.

By the time the pair return nearer to Kaylee, Mal pushes his windblown hair away from his face with a grin. "Can y' help me a bit?"

Help seems to indicate holding the reins and bridle after they are removed from Tequila while Mal unsaddles him.