Updating the percentage has always updated for all assignees as far as I know. But I agree that marking "done with my part" is harder in the new home.
In both the My Work and My Tasks widgets, if an item is assigned to multiple people, clicking on Start Task > Mark As Done will give you the option to choose Done With My Part or Closed. At first, I wished it would give you the dropdown menu like the old home did, but this forces the user to decide whether or not to close the whole thing. I can see the logic of this new approach.
I've only tested this in WF Preview and not on any items assigned to me, but I'm interested in hearing other people's experiences.