In my settings I set my friendly formation as ‘friendly1’ which is the name of my reserve formation, which I always use for friendlies. So I though it would automatically set my formation to this one whenever I accepted (or created) an invitation for a friendly.

However, what has been happening is that if I accept a friendly invitation without setting a particular formation, the AI will set my default formation, which is the main team. I wonder if I’m doing something wrong.

No, default is always the default formation for every game. If you want to use another formation for a game, you have to select that one.

If you have several invitations, you can use the ‘accept all’ feature (and select ‘friendly1’ for all).