Most of the time it is a save file check. But, if they are suspicious about other parts of your account like Auric Cells and/or Shards they will check their logs and determine whether your auric cells/shards are hacked or not.
And as for save file checks, I don’t know if the in-game report system is any different from the ticket system on their website. I’d reckon they have the same effectiveness, but other people think otherwise.
And your question is pretty vague, so please try to be more specific next time.