I'm not sure exactly what the cause of this is, but it's game 4610345. If I have Coins of the Realm on my Tavern Mat, I believe there's an effort made to not make me stop and click "done reacting" unless there's a real need for that (like you're in the middle of a Throne Room chain or something like that). I don't see anything on this board that would prompt me to need to keep telling the client I don't want to call my Coins yet, yet I have to do this a lot more than just at the end of my Action phase.
I think the real fix for this is an autoplay where it only asks you if you want to call a CotR when you have zero actions remaining, but maybe there's something weird going on that this sheds light on.
EDIT: I think it might just be whenever I play an Overlord as something. I understand why it's coded this way, but maybe it's really easy to check whatever card Overlord/BoM/whatever else is mimicking, instead of what card it actually is? If so, this seems like a welcome change until the autoplay is done.