If you kick-mute someone from a room, no automatic annotation is made on their profile, though one is made if you suspend them from a room.
For tracking/moderation purposes and to match the suspension feature, an annotation should be automatically created when someone is kicked.
As I commented and Snow screenshotted, a log of kick-mutes is indeed shown, but is in a separate page from the one that shows suspensions and annotations.
There is one major caveat to having kick-mutes be on the same page as the latter: unlike moderator privileges, room owner privileges are given out quite trivially compared to moderator privileges. One can become a room owner simply by creating a room or by being the sole active user in a room whose current room owners are inactive. One can also become one just by being appointed one by someone else, such as by a friend in a room that's used for fun.
By nature, when a privilege is given out trivially, it's going to be used frequently. For instance, in the aforementioned "fun" rooms, it often happens that users just kick each other for fun rather than because of an actual violation of the room rules. Having these actions listed in the same list as (and counted in the same number of) actual, serious moderator suspensions and annotations isn't something that should be done in my view.
I think the current system of having them on separate pages is good. The system does a good job of separating these room owner-level actions from the moderator actions of suspensions and annotations. Note also that the system will also automatically notify moderators if a user is repeatedly kick-muted; in that case, if moderators want a note on the same page, they can just annotate them then. One useful change, though, would be to link to the kick-mute list from the suspension and annotation list.
An alternative would be to list them on the same page, but allow the page to be filtered to different types (annotations, kick-mutes, suspensions, etc., or any combination of the above). If this is done, then only annotations and suspensions should be counted in the displayed number.
This question has arisen due to an action I took in the SE Lobby. A 1-rep user started throwing poop around the room (their words) and I asked them to stop, when they didn't, I naturally kicked.
We see a great deal of users in the Lobby rooms who are transient, they say a few words and we never see them again. I know that kicks are reported on someone's chat profile, so I didn't bother creating a formal annotation on this users record (especially since we probably won't see them again).
Kicks are hidden within "Permissions" moderator/RO screen for the user, which isn't intuitive and one of those places you wouldn't look unless you know where to look.
These kick events should, I feel, be included on the main chat annotations screen and not hidden away in a separate screen. There should also be a link to the last message from the kicked user so that interested parties can simply inspect the transcript for context.
