How do I make in-app purchases appear within my apps on all of my devices?
Assuming you've used the same Apple ID on all devices you shouldn't have a problem. However, you will need to restore the in-app purchase on all devices you didn't originally use to make the purchase.

To do this, you will need to navigate around the app and look for an option labelled something like restore in-app purchases (or similar). Many apps will put this option within their own settings page, but I can't advise you exactly where it will be for this app (as I don't personally use it).

If you can't find an option anywhere to restore the in-app purchase, I would go to their dedicated iOS forum page and ask for help.