How to reference a view using entity reference field type?
Sounds like you know what your doing. Like you say either create a 'view mode' in your content type or create a view. All you have to do with the view is create a relationship (under 'relationships' in the advanced section) to get your entity reference and set a filter for the tutor.

Tried to find something similar to your issue, hope it helps. How to use Entity Reference and Views