What do those evaluating fellowship candidates look for before accepting them to join their research group/department?
I would say several points related to the candidates such as


How much in average do candidates publish per year?
Where do they publish? 
What conferences they presented their papers in?
What are the impact factors for journals they publish in?
What new research questions or directions do they have? 
How much citations did they received?
With whom in the group they can collaborate?
What funds do they have or can bring? 
What experience in writing proposals do they have?
What are some similar proposals that received funds?
Where their research is going in the next 5-10 years?
What industry or academic experience do they have?
What skills do they have?
Can they enhance research group diversity? 
Can they teach, present and discuss well?