Search api auto complete grouping issue

The Search API is not equipped to retrieve search results that way. You will either need something like the Search API Grouping module → or execute several searches, one for each datasource/group. In any case, you’ll probably need to provide your own custom suggester plugin for this (or override the “Live results” one).
If the code is neat enough, and other people also express interested, I’d be willing to consider something like that to the module, so I’m leaving this open in case someone wants to suggest code for this.