We caught the same limited express back to Kagoshima. A hint for anyone anyone considering booking a seat: there are good seats and less good seats on the Ibusuki no Tamatebako, depending on if you want a view, or some legroom, or a bench on which to rest your lunch, etc. If you are able, reserve seats as early as you can. We reserved seats on the English website, but it didn't appear to allow us to book particular seats so we ended up jammed on the least scenic side of the train with little to no room for our bags.