Faceted Search Block displays values from other facet blocks
I finally got the answer by myself. Never thought it would be such a little setting: 

If you're going to index a "text field" (and maybe going to enable the related facet block), make sure the text field is declared as string instead of fulltext.

Just go to -> Search API >> edit the correlating index >> Fields 

and check the textfields. Following this you just have to re-index the items.