In today's update: the Kill Count Book will now track boss and minigame completion times! You can view the new section using a button which you'll find at the bottom of your Kill Count book!
For a time to register, there's a requirement that the player completing the kill does 95% or more of the damage to the NPC. There are exceptions for CoX, ToB, and the Nightmare. In those places, the entire team will have a shared time registered. This may be reworked, but for now it seems like the best way to ensure the highscores are as fair and competitive as possible.
You can toggle time notifications for individual bosses in the same way as in the killcount section; by clicking the entry for the boss and choosing whether you'd like to show or hide notifications. You can also sort by time completed or alphabetically using the settings button at the top right of the book.
What about my old completion times?
To add your personal best for the Chambers of Xeric, simply open up the scoreboard near the CoX entry and it will be added to your kill count book. For other bosses and minigames which were previously timed, there will be no preloaded times.