Theme based altering of default image-style for the same node-type and view-mode
Well after reforming my question 3 times and rethinking what the actually question should be like to find a solution, I came to the conclusion that the Domain_views module is completely broken (ALL Domain views fields always output the default Domain ID/name/path no matter what), and that the theme layer node--view-mode.tpl.php altering approach is not generic enough to have this functionality in other use-cases.

So I found a nice trick, which maybe also helps others to change field styles in a given steady node-type and same view mode under certain conditions, but it needs Views module:

Use the Views_conditional module and use your fantasy to get the needed result. :-) That easy! 

In my case I was able to turn off the Domain_views module completely (finally!) and have used the absolute path setting from the content:path views field to change the image-style under the condition, that the path includes a given pattern of one of my domains. I have 2 image fields (excluded in Views) and a conditional field showing one of them if needed, e violá! :-) My image style changes in the 2 different domains by the same given node-type and node-view-mode! Awesome

Views as a full node view mode designer... I never stop learning. ;-)