I had to use the hint booklet to understand where to put each plate in the crypt but even reading the solution I didnt understand what's the logic?

Please explain

CAREFUL: For those that haven't played the game yet, please leave this thread now as it contains a spoiler. 

There are two ways to solve the puzzle. The dumb way is to google the mentioned Saints. You will learn about the places where they were active. Saint Adomnan is actually called Adomnan of Iona. So you have to put the Adomnan plate in the Iona Abbey mural. 

The smart way is to go on the first floor and in the gallery you check out the pictures of the Saints. You notice a list of Saints and underneath the pictures are plates with names. I think it is a list of 10 saints or so. Only four are relevant but all the Saints that you find as plates are found there. Let's take Saint Cuthbert for example. In the gallery you will learn that his name is Saint Cuthbert of Lindisfarne. Hence, in the crypt, you connect Cuthbert to the Lindisfarne mural. 

So to sum it up: you solve this puzzle by connecting the Saint to the place he was known for. 

I am guessing you either didn't notice these pictures in the room description and did not examine them OR you did not make the connection :)