Thanks David, now everything works as expected! I will add that linking the boxes together in the workflow editor I found intuitive and without problems, however the descriptions and functionality of various different triggers and actions I found very confusing and assuming a lot of knowledge that I didn't have. I'm still confused why a Fallback Search trigger somehow applies only to Contact results (or at least another help post here seemed to indicate that).
But now I have all I need and somebody else can preach the usability to you