Well, at least people still come to you as a manager, which can be considered as a successful trait as a manager.
Besides of people who over communicate, there are always people who don’t communicate. They don't check their emails timely, if they do they don’t reply in time, or they never mention it to you after they had meetings with other team leads which requires you to assign them stuff based on that ... Argh, sometimes those can be way more trickier. If there’s one like this in your team, and s/he happens to be very good at what they do except communicating, then you might have to treat them differently with a bit more freedom in their style. You will need to make sure they they can be not talking to anybody else, but they have to come to talk to you, report to you and let you know how’s going with the project, especially when there’s a time pressure. Otherwise, the team might be better off without them.