In what situations, when reacting to impressions, are the signals sent directly from the thalamus to the hypothalamus?
As @Pyssling states, it has to do with fear, and how we process situations that are potentially dangerous. There is a distinction between the two concurrent processes that you describe, that go under the title "short route vs long route" or "low road vs high road" (possibly more titles). 

The short route (or low road) is the immediate process/reaction/response, which would enable os to avoid death in certain situations - This works on an instinctive level. The long route (or high road) is the process/reaction/response that could be defined as a thorough evaluation of the input/signal that we receive. 

This site has descriptions and images that can be read on three "levels of explanation", and I find them highly informative. 
http://thebrain.mcgill.ca/flash/a/a_04/a_04_cr/a_04_cr_peu/a_04_cr_peu.html

Here is a youtube video on the subject "How fear is wired in the brain" that deals with the same topic. https://www.youtube.com/watch?v=vl_B6nz3UOQ

I am in no way an expert and have stumbled upon these sites based on personal interests, so I do not know if someone may be able to criticize their validity / quality, but I found them excellent.