no response from the OP to clarify the question.so, imo both options are probably half baked attempts by the two parties that should have a drawing by your architect/designer to ensure this detail is thermal bridge free.
stopping the 'black' - your builder needs a basic science lesson.
your window company are very brave to claim that there will be no cold bridge between the window and wall build-up - unless a thermal assessment has been carried out?
Thanks lowCO2design for taking the time to respond. I hadn't asked the architect so that's what I did based on your post.
He said that we didn't need the warm boards as we have dry lining already. The architect thought the previous problem with mildew and condensation was due to the old aluminium single glazed windows.
We got them installed on Friday and we're delighted with them. We got Carey Glass triple glaze Iroko hardwood. There has been no condensation at all. Previously you couldn't see out the window properly with the amount of condensation.