Hello David and welcome.
That is a good question and one that I have thought about also; but unfortunately we don't have any sources that give definite answers. We do know that each mint had an official in charge called a Procurator Monetae and these men most likely received direction from an Imperial bureau called the A Rationibus which later became the Comes Sacrarum Largitionum. There is an ancient source (I can't recall off the top of my head) that refers to a bust of the new Emperor being sent to each city so that people would know what the Emperor looked like, so I imagine the bureau responsible for minting would also send an example of new types to be minted. I don't believe that the Emperor would have been involved to a large degree, but I am sure designs would have been shown for his approval. For example, Constantine was in Constantinople quite a few times in the years 325- 330 as there was a lot of building going on prior to the dedication in 330 and the mint of Constantinople issued coins ( GLORIA EXERCITVS, GLORIA ROMANORVM, LIBERTAS PVBLICA, SPES PVBLIC and finally the DAFNE coins) specific to that mint that no other mint issued, so I expect that Constantine had more to do with this situation than merely signing off on some coin designs. Of course, things like control marks would have been up to each workshops discretion, maybe approved locally by the procurator.
