But when the staging, singing and playing come together, whether in exuberance or sorrow, I was happily reminded of another musical about music that originated at the Atlantic: “The Band’s Visit.” (David Yazbek, that show’s songwriter, is credited here as a creative consultant.) In such moments — the hypnotic “Chan Chan,” the ear-wormy “El Cuarto de Tula,” the heartbroken “Veinte Años,” the gorgeous “Drume Negrita” — you really do feel the past harmonizing with the present. What Compay says is true: “Old songs kick up old feelings.” Even, as in the showstopping and, yes, scorching “Candela,” with a flute.