You would need to contact the app developer to find out what's wrong. Normally when you add a subscribed calendar without an app it will push to your other devices. This article explains how to do this on your Mac: http://support.apple.com/kb/HT5029.
Well, this certainly wasn't the most elegant way, but at least I got the calendars on all my devices now.
I subscribed to them all on my iPhone, went to Settings > Mail, Contacts, Calendars > Subscribed Calendars and copied each of the servers into a note. I then deleted all the subscriptions.
Back on my Mac I added the calendars manually (alt+cmd+S), which caused a bit of a problem at first, but I figured out it was because the server addresses didn't contain "https://". That way I was able to configure colours, and updates easier and they are now on all my devices.