No results behavior in Views not working when referencing another field after cache clear
I replicated your scenario and its working fine for me.

Here is what I did.


In Taxonomy I added a Vocabulary called "Sermons", I added an image
field called "tax image"
I added a term name of "Mega Man" to Sermons, and uploaded a
mega man picture to the "tax image" field.
Created an Article with title of "Enter Shikari is awesome" which has "Article Picture" as a field and I uploaded a picture of the band. Term Ref "Mega Man"
I Created another Article with title "Woooo" this time I did not upload any image to the "Article Picture" field. Term Ref "Mega Man"


Now in Views


In FILTER CRITERIA I added Content Type Is one of Article (so it only shows Article nodes)
In RELATIONSHIP I added Content: Taxonomy terms on node 


Check marked "Sermon Series" 
Check marked Require this relationship. 






In FIELDS and I added the "tax image" 


checked exclude from display.

In FIELDS I added "Article Picture" 


No Results behaviour I put the token [field_tax_image]






I put a cache of 1 hour. 


So here is what my View looks like




I added another Article with title "Kewl its working!!!" with Term Ref "Mega Man" and left the "Article Picture" field empty. 
I Cleared the cache (since my view is cached, it won't show "kewl is working!!! until I clear it).


RESULT AS EXPECTED Kewl its working!!! and Wooo do not have Article Pictures, so Mega Man (tax image) shows up.