Yes, AFAIK that is the expected behaviour. Malkovich log is visible to observers, hidden only to your opponent, thus if you need to log out for some reason the site sees you as a general observer and displays Malkovich.
It has already been discussed here some time ago with arguments for both possibilities (if you are interested)
If you dislike such design you can also vote here:
https://ogs.uservoice.com/forums/277766-online-go-com-suggestions-and-feature-requests/suggestions/14696247-make-a-private-malkovich-log-separate-from-current