Show Taxonomy Terms belonging to search_api search result nodes
This may have drawbacks but I had a situation where i wanted to show the multiple tags that related to content that i had indexed.

Having looked through https://www.drupal.org/node/1378656 i opted to try by using https://www.drupal.org/project/views_field_view

Happy to report it worked

Here is the recipe:


create a new View based on Content for types involved and set just the relevant 'term' field as the display (you don't need to create any views displays).
set Contextual filter to nid with 'provided default value = raw value from url' (outcome should be if you enter the nid you should see relevant tags in preview). Save
install/enable https://www.drupal.org/project/views_field_view
over in the view that is rendering the search results (searchapi) 
made sure you have Indexed Content: Node ID field already in your Fields, and set to not display
add a new field of type Global: View
in the 'view settings' of this field, find the view you made above, set the right display or use Master if you didn't make any (because you didn't need to), 
in Contextual Filter, check your Replacement Patterns where you should have [%nid] == Indexed Content: Node ID (rendered), and enter [%nid]
save and I hope you get to smile like i just did.