That's misrepresentation of the situation, the crime is not installing an app(nobody is sentenced for the crime of using an app) but being a member of an organisation that is deemed illegal and the app is considered evidence for membership as it was members exclusive app. Think of it as if being an Uber driver was illegal, then having the drivers app can constitute as a good reason for suspicion of you being Uber driver and you might be held until you receive a sentence or cleared from wrongdoing.

The problem here was that the Turkish authorities were "a bit too liberal" on what constitute of using the App in question, that is, they mistakenly assumed that making HTTP request to the App's server is a good indicator of being a user.

Unfortunately this is the way that the Turkish government operates since many years, they first lock you in and you fight back for years until you prove your innocence. What's even worse is that you can't really get good compensation for it, you just suck it up and move on.