They are not side and top printed at the same time
If you check out the configuration page, you will see an option to "Upload Your Own Artwork" - they say on the site that this option gives you "total control" over the print on the caps. If you download the template file, you can use either Inkscape or Illustrator to design the legends on the caps to your liking. It takes time, but if you are looking for something specific that you can't find anywhere else, it might just be worth it.
If you don't want to invest your time without knowing 100% for sure they will be able to do this, send them an email and ask. It might take a little longer and cost a little more, but you will get what you want.