Ok, so here's the deal.
The tower got shut down for a while due to safety concerns, but it's renovated now and back up and running. My class missed it during plebe summer (because it was shut down), but that was back for 2014 and 2015 at least. Not sure about 2013. So, plebes now do it during plebe summer and 3/C swimming.
Class by class, the requirements are:
4/C: 200m swim for time (final test, 100%=2:45), 40 foot underwater swim (swimgear), various form tests (cross the 25m under a certain number of strokes in a particular form).
3/C: 400m swim for time (final test, 100%=6:10), 50 foot underwater swim (cammies), various form tests, float test, making a flotation device out of cammie pants, and the tower jump. Where things are different is that the tower jump used to be 10m and pass/fail. Now, it's on a graded scale: jumping off the 10m platform is a 100%, the 7.5m=80%, 5m=70%.
But the instructors will guilt your entire section (and your section will peer pressure you) into jumping off of the ten anyway, so don't worry about the other grades.
2/C: "Thirty year." You have thirty minutes to swim, in khakis, a certain number of laps without touching the wall. The minimum to pass is 700m, a perfect score is 1500m. This may not sound bad, but it's a lot harder with 5+ people a lane and getting choked/drowned by your khakis. 2/C Swimming is only 8 weeks long and the rest of that semester you take a physical conditioning class (which is academic, not really a PE, and has a written test at the end).
Swimming isn't really something to worry about. I had never swam for time in my life before USNA and was not super comfortable in the water. I still passed, and managed to not do horribly.