That's not a bug, it's a feature. There is no subscription, neither monthly nor yearly, for this wonderful app called Diarium. It's just a one-time payment for every platform you are using it on. That's it. Other apps are asking you for a subscrition which you have to pay for regularly. If you prefer this type of money burning, then Diarium isn't for you.
Everything about the how and why you can find in the Pro FAQ. Just read it. 😉