How to: SearchEverywhereContributor

I want to create a new search which pulls data from a remote REST API, which returns a JSON with all suitable results.

So far I have a custom SearchEverywhereContributor class, which display a new tab in the Search UI.
But where do I implement the querying of the API and where and how do I "send" the data to results list of the searcheverywhere UI?

Thanks in advance!