Questions about Puffin sex are frequent out here (Machias Seal Island), often prompted by the fact that Razorbills can be seen copulating VERY often and throughout the season on land. The short answer, as Bob said, is Puffins do it on the water.
Having said that, last year was an exception, with a lot of Puffin copulation reported within the colony.
Prior to that I had only caught the act on land twice in 18 seasons.As to the presumed male-female Puffin configuration, Bob is likely correct. However, in a study of Razorbills of known gender, it was found that the bird on top was always male but the bottom wasn't always female.