Both on my iPad and iPhone. You play a minion, takes a moment for it to actually set, then try to do hero power but not highlighted for a few seconds.
I have been having the same issue ever since Rastakhans Rumble came out. I never had lag issues before that. I mainly play on my pc. During almost every turn, I might be able to make a few moves with no issue but then I’ll go to play another card and the action doesn’t happen for a minute and then it plays. Other graphics are still moving around the board and so the whole screen doesn’t freeze, just the card/play. I have lost a few matches because of not being able to complete a turn due to it timing out. So yeah the burning rope still goes and ends my turn while I sit there waiting to be able to play another card or take another action.